Chasuta Anukoolthamchote - University of Hawaii€¦ · electricity load, specifically in light of increasing levels of solar saturation in Oahu. It is found that, regardless of the

ESSAYS ON SOLAR PHOTOVOLTAIC ADOPTION AND ELECTRICITY

CONSUMPTION PATTERNS: EVIDENCE FROM PARADISE

A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE

UNIVERSITY OF HAWAIʻI AT MĀNOA IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

PHD

IN

ECONOMICS

AUGUST 2017

By

Chasuta Anukoolthamchote

Dissertation Committee:

Denise Konan, Chairperson

Lee Endress

Timothy Halliday

Nori Tarui

Anthony Kuh

Dora Nakafuji

Keywords: solar PV adoption, rooftop PV, PV penetration, electricity consumption

behavior, electricity demand, renewable energy, technology diffusion

ii

Copyright © 2017 by

Chasuta Anukoolthamchote

iii

ACKNOWLEDGEMENTS

I would like to thank Hawaiian Electric Company for the amazing work collaboration

opportunity, Denise Konan, Dora Nakafuji, my committee, and the Renewable Energy Planning

Team for their invaluable guidance, and Talin Sokugawa and Jonathan Page for their help and

suggestions. Most of all, I would like to thank my family and the Stearns family for their love

and support throughout my dissertation. Any remaining errors are my own.

iv

ABSTRACT

This dissertation studies several aspects of the widespread adoption of solar photovoltaic (PV)

and how such rapid adoptions has been impacting the electric grid and consumers’ electricity

consumption. Chapter 1 addresses the underlying determinants of variability within net

electricity load, specifically in light of increasing levels of solar saturation in Oahu. It is found

that, regardless of the level of solar power generation, customer mix exerts a significant impact

on the pattern and level of net load from hour to hour. The PV penetration elasticity of volatility

of net electricity load shows that if the level of PV penetration in a certain area were to increase

by 100%, the volatility of net electricity load on that area would be expected to increase by 3%,

ceteris paribus. Taking into account the increased PV adoptions, the dynamic between residential

and commercial electricity use patterns immensely reduces issues resulting from high variability

in solar power generation.

To better support the integration of solar PV and other distributed energy resources, it is crucial

to understand the evolution and diffusion of solar PV technology. In Chapter 2, we examine

adoption trends and characteristics of residential PV adopters in Oahu, Hawaiʻi. Homes having

PV installations are found to be newer, larger, more energy efficient, and less costly per square

foot than those without a PV installation. The analysis also reveals that early PV adopters,

defined as those installing PV systems before 2012, are generally older, wealthier, more likely to

own their own home, and had higher levels of educational attainment than do their contemporary

counterparts.

To better understand the true impact of solar PV adoption on electricity consumption, Chapter 3

evaluates whether residential PV adopters exhibit changes in their energy demand, including

responsiveness to price and weather fluctuations, following installation of PV systems. An initial

examination of pre- and post-installation consumption trends within the sample dataset indicates

that PV households increase their electricity usage by approximately 3% in the first year

following PV adoption, with this growth rate gradually decreasing in ensuing years. Conversely,

non-PV customers exhibit consistently decreasing electricity consumption over the observed

time period.

v

To more clearly understand the impact of solar adoption on electricity consumption, we divide

PV households on the basis of their PV sizing decisions. Towards this end, we first define a set

of three distinct PV sizing categories: Net Import, those who “under-sized” their PV systems;

Net Zero, those who sized their PV system to offset roughly 100% of their pre-solar

consumption; and Net Export, those who install “larger than necessary” PV systems. Using this

grouping, we find that the majority of households within the sample dataset fall under the Net

Zero group, with only 2% classified as Net Export households. It is observed that Net Import

households decrease consumption by approximately 4% in the first year following PV adoption.

Conversely, Net Zero households consume more energy after PV installation, increasing their

electricity consumption by approximately 8% in the first year following PV adoption. Net Export

households exhibit the largest post-installation increase in consumption, which increases by over

30% in the first year following installation and by over 50% by the end of the fourth year post-

installation.

We further estimate electricity demand showing that household responsiveness to price and

weather variations is found to differ before and after installation of solar PV systems. Following

PV installation, household consumption becomes more sensitive to price variation, estimated

between -0.25 and -0.17. Clear differences are also observed between the various PV sizing

groups in both their pre-solar responses to price, and the impact of installation on their price

response. Electricity consumption in Net Import and Net Zero households becomes more elastic

to price variations following PV installation. Conversely, Net Export households become less

responsive to price after installation of “over-sized” PV systems.

vi

TABLE OF CONTENTS

Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

List of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

1 Increasing Solar PV Penetration & Fluctuation in Net Electricity Consumption. . . . . . . 1

1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Literature Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Data Description & Summary Statistics. . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.1 Time-of-Day & Customer Mix. . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.2 Weather Variations & Solar PV Penetration. . . . . . . . . . . . . . . . . . 8

1.4 Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5 Empirical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.5.1 Additional Result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.6 Conclusion & Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Evolution of Residential Solar Adoption in Oahu, Hawaii. . . . . . . . . . . . . . . . . 19

2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Literature Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 Data Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.1 Data Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.2 Data Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

vii

2.3.3 Summary Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 Descriptive Evidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4.1 Solar Adoption Trend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4.2 Characteristics of Adopters & Non-Adopters. . . . . . . . . . . . . . . . . 28

2.5 Structural Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.6 Empirical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.7 Conclusion & Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 Impact of Solar Adoption on Residential Electricity Demand. . . . . . . . . . . . . . . 37

3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 Literature Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3 Data Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.1 Data Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.2 Summary Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4 PV Sizing Decisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.5 Consumption Trend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.5.1 Comparisons: Pre-Solar VS Post-Solar Consumption Behavior . . . . . . 49

3.6 Statistical Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.7 Empirical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.7.1 No-PV & PV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.7.2 No-PV & PV by Sizing Group. . . . . . . . . . . . . . . . . . . . . . . . 54

3.7.3 Additional Findings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

viii

3.8 Conclusion & Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

A Tables for Chapter 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

B Figures for Chapter 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

C Tables for Chapter 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

D Figures for Chapter 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

E Random Sampling Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

F Tables for Chapter 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

G Figures for Chapter 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

H Additional Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

ix

LIST OF TABLES

A.1 Summary Statistics of Variables at Distribution Transformer Level. . . . . . . . . . . . 59

A.2 Volatility of Net Electricity Load by Time, Seasons, and Year. . . . . . . . . . . . . . 60

A.3 Empirical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.4 Empirical Results – Daytime Only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

C.1 Summary Statistics & Difference in Means. . . . . . . . . . . . . . . . . . . . . . . . . 69

C.2 Marginal Effects for the Logit Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

F.1 Summary of Electricity Demand Studies. . . . . . . . . . . . . . . . . . . . . . . . . . 80

F.2 Summary Statistics of Monthly Electricity Usage – No-PV & PV. . . . . . . . . . . . . 81

F.3 Summary Statistics of Other Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . 81

F.4 Summary Statistics of Monthly Electricity Usage – By PV Sizing Group. . . . . . . . . 82

F.5 Empirical Results for Electricity Demand Model (3.8) and (3.9). . . . . . . . . . . . . . 83

F.6 Empirical Results for Electricity Demand Model (3.10) and (3.11). . . . . . . . . . . . . 84

H.9 PV Sizing Categories - Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . 100

H.10 Number of Households with Additional Solar PV Installations. . . . . . . . . . . . . 101

H.11 Transitions across Sizing Groups – PV Households with Additional Systems. . . . . . 101

H.12 Number of Households with & without Solar Hot Water Heater (SWH). . . . . . . . 101

x

LIST OF FIGURES

B.1 Annual Solar Installed Capacity by Customer Segment. . . . . . . . . . . . . . . . . . 63

B.2 Variations in Net Electricity Load – Residential. . . . . . . . . . . . . . . . . . . . . . 64

B.3 Variations in Net Electricity Load – Commercial. . . . . . . . . . . . . . . . . . . . . 64

B.4 Variations in Net Electricity Load – Industrial. . . . . . . . . . . . . . . . . . . . . . . 64

B.5 7-Day Net Load Profiles – Residential, Commercial, Industrial Areas. . . . . . . . . . 65

B.6 Relationship between Temperature and Humidity – Sun & No Sun. . . . . . . . . . . . 66

B.7 Average Solar Irradiance by Time-of-Day – Winter & Summer. . . . . . . . . . . . . . 66

B.8 Volatility of Net Electricity Load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.9 Net Electricity Load of 4 Sample Transformers. . . . . . . . . . . . . . . . . . . . . . 68

B.9a Residential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.9b Commercial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.9c Industrial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.9d Mix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

D.1 HECO/AWS Virtual Gridded Data Map – Oahu. . . . . . . . . . . . . . . . . . . . . . 71

D.2 SolarAnywhere Data Map – Oahu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

D.3 Estimated Monthly Solar Irradiance – A Sample Grid-Tile Data Point. . . . . . . . . . 72

D.4 Annual & Cumulative PV Installed Capacity of the Sample. . . . . . . . . . . . . . . . 73

D.5 Average PV Price Modules & Total PV Installation Cost. . . . . . . . . . . . . . . . . 74

D.6 PV System Size Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

xi

D.7 Percent Energy Offset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

D.8 Housing Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

D.8a Age of Home. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

D.8b Home Value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

D.8c Home Size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

D.8d Baseline Consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

D.8e Energy Intensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

D.9 Households’ Demographics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

D.9a Median Age. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

D.9b Median Income. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

D.9c Homeownership. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

D.9d Education. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

D.9e Family Size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

G.1 Electricity Prices & Brent Crude Oil Price. . . . . . . . . . . . . . . . . . . . . . . . . 85

G.2 Average Monthly Electricity Usage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

G.3 Percent Energy Offset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

G.4 Solar Installation Trend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

G.5 12-Month Pre-Solar Monthly Usage. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

G.6 PV System Size Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

G.7 Average Annual Usage & Percent Year-over-Year Change. . . . . . . . . . . . . . . . 89

G.8 Solar Consumption Trend – 2 Years Before & 4 Years after Installation. . . . . . . . . 90

xii

G.9 The Rate of Change in Electricity Consumption after PV Installation. . . . . . . . . . . 90

G.10 Percent Exported Energy Relative to PV Energy Production. . . . . . . . . . . . . . . 91

G.11 Net Monthly Electricity Consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . 91

H.1 PV System Size Distribution – Sample VS Population (Oahu). . . . . . . . . . . . . . 92

H.2 Gross Electricity Consumption Calculation. . . . . . . . . . . . . . . . . . . . . . . . 93

H.3 Average Monthly Electricity Consumption – No-PV & PV. . . . . . . . . . . . . . . . 94

H.4 Average Monthly Electricity Consumption – No-PV & PV Sizing Group. . . . . . . . . 95

H.5 Percentage Change from Pre-Solar Usage – Net Import . . . . . . . . . . . . . . . . . 96

H.6 Percentage Change from Pre-Solar Usage – Net Zero . . . . . . . . . . . . . . . . . . 97

H.7 Percentage Change from Pre-Solar Usage – Net Export . . . . . . . . . . . . . . . . . 98

H.8 Percentage Change from Pre-Solar Usage – Separated by Percent Energy Offset. . . . . 99

1

CHAPTER 1

Increasing Solar PV Penetration

& Fluctuation in Net Electricity Consumption

1.1 Introduction

Achieving adequate supplies of clean energy for the future is a great societal challenge. Nowhere

is this need more urgent than in Hawaiʻi, where electricity prices are three times higher than the

U.S. mainland average.1 These high energy costs have a large impact on Hawaiʻi’s economy,

imposing a major burden on both local customers and businesses. As the demand for energy

continues to grow, Hawaiʻi has focused on transitioning to clean and affordable renewable

energy sources.

Solar photovoltaic (PV) adoptions have grown exponentially within Hawaiʻi. Figure B.1

illustrates annual and cumulative installations of solar PV by customer segment on the island of

Oahu.2 However, the widespread adoption of solar PV poses a number of unique challenges to

electric grids which must integrate large quantities of solar generation. Solar output driven by

solar irradiance is variable and intermittent, and cannot be adjusted by the utility system

operator. Rapid swings in solar electricity can lead to temporary mismatches between energy

supply and demand. Therefore, additional dispatchable system reserves and backup capacity may

be necessary in order to maintain system reliability.

This study evaluates the impact of intermittent solar power generation under variable climate

conditions on the electric grid of the island of Oahu from September 2010 to May 2014. The

standard deviation of net electricity load is used as a representative variable for volatility in

electricity generated by the utility.3 An empirical analysis is performed employing a unique

proprietary data set detailing electricity net load and solar penetration levels at the distribution

1 For example, in June 2014, Hawaiʻi’s electricity price was 38.7 cents per kilowatt-hour (kWh) while the U.S

Mainland average was 12.9 cents per kWh. 2 The megawatt installed capacity shown in figure B.1 is measured by the total "nameplate" capacity of solar PV of

fully executed applications. 3 Net electricity load is defined as the amount of energy met by utility generation.

2

transformer level.4 It is found that higher levels of PV penetration increase variability of net load.

This effect is most pronounced during daytime hours when the sun is out.

The data set employed in this study also contains detailed information on the customer mix of

each distribution transformer. Using this information, we examine the combined effect of

customer diversity and increased PV penetration on the shape of load profiles. It is found that,

regardless of the level of solar power generation, customer mix exerts a significant impact on the

pattern and level of net load from hour to hour. In residential-concentrated areas, net load

exhibits two distinct peaks – morning and night. This is reflective of the underlying consumption

behavior of residential customers who typically leave for school or work in the morning and

return in the evening. Conversely, commercial- and industrial-concentrated areas exhibit a single

midday peak corresponding to regular business hours.

The different distribution transformers considered in this study are observed to have a diversity

of load patterns, depending upon their mix of customer classes. While the shape of their load

profiles is primarily influenced by the customer mix and time of day, their load variability at

each time period is remarkably the result of increased PV penetration level. Our result indicates

that customer mix is the key driver influencing net load behavior in each area. Taking into

account the increased PV adoptions, the dynamic between residential and commercial electricity

use patterns immensely reduces issues resulting from high variability in solar power generation.

Over the past few years, Hawaiian Electric Company (HECO) has deployed several solar and

wind monitoring devices at various locations throughout its service territory. These tools provide

estimates of solar irradiance, wind speed, as well as temperature and relative humidity. In this

study, we employ these measured meteorological variables along with seasonal variations to

identify both the impact of climatic variations on electricity use, as well as their impact upon

intermittent solar power generation. We find that wind speed negatively affects net load

variability, whereas temperature exhibits a significant and positive impact. Given the semi-

homogenous climate in Oahu, we further investigate the effect of temperature while taking into

account humidity values in the air. Our results show that when humidity is high, increasing

4 A distribution transformer provides the final voltage transformation in the electric power distribution system,

changing voltage level between higher transmission voltages and lower distribution voltages. In the sample of this

paper, there are one to three distribution transformers in a substation depending upon the size of cities or towns

which the substation supplies power to.

3

temperatures cause net load variability to increase at a diminishing rate. This is largely due to

consumers’ electricity consumption behaviors. Most consumers consume more energy by turning

on cooling electrical appliances when the temperature rises. This effect persists when both

temperature and humidity are high. The effect of increases in both factors, however, increases

the volatility in net load at a decreasing rate.

The seasonal variations are captured through time-of-day and season dummy variables. Our

results indicate that the net load exhibits higher volatility during the day in winter months.

During the winter, Hawaiʻi’s temperature and solar radiation levels are generally lower than

those experienced in the summer. Changes in temperature between day and night will likely

induce consumers to switch on air conditioning during the day and off during the evening.

Moreover, the solar output will likely fluctuate more due to the high intermittency of solar

resources in the winter, resulting in larger volatility in net electricity load.

The remainder of the paper is organized as follows. Section 1.2 reviews related literature. In

Section 1.3, we introduce the details of our unique data set and describe how each variable is

calculated. Section 1.4 then presents the econometric models used in this analysis. Estimation

results are reported in Section 1.5. The concluding remarks and discussion are given in section

1.6.

1.2 Literature Review

Several studies address the value and impact of the intermittency of solar electricity generation

upon electric grids (Hansen, 2007; Fthenakis et al., 2009; Joskoaw, 2011; Stein et al., 2012;

Stewart et al., 2013). These studies claim that, in addition to certain characteristics of PV panels,

various other factors affect solar electricity output, namely, the time of day, change of seasons

and weather variations. As examples, Mills (2013) and Baker et al. (2013) examined the

economic value of variable renewable generation and concluded that the value of new

generations of PV can decrease as the level of penetration rises. Because there are additional

costs associated with backup generation and solar intermittency, such costs can be minimized if

utility companies know how to better operate the electric grid. If operations and investments are

optimally managed in consideration of PV penetration, then additional costs can be

comparatively small.

4

Consequently, forecasts of solar power have become necessary for the integration of fluctuating

renewable energy into the grid. Various emerging studies have considered the ability to

accurately forecast variability in renewable resources, such as wind and solar (Perez et al., 2010;

Lorenz et al., 2011; Marquez and Coimbra, 2011; Mathiesen and Kleissl, 2011). Because solar

power typically exhibits different generation characteristics as compared with power produced

by conventional sources, more precise solar forecasts will enable electric system operators to

better manage electricity generation in spite of fluctuating solar output.

Along with the volatility of solar output, fluctuations in electricity usage also depend upon

climatic conditions. The influence of weather variations has a demand side impact on the

electricity market. Weather can have diverse effects on different sectors of the economy. Moral-

Carcedo and Pérez-García (2015), for example, find that changes in temperature have a large

effect on the electricity demand in Spain’s service sector. On the other hand, weather variations

have not been found to influence activities of the industrial sector, remaining highly and

positively correlated with residential electricity demand (Amato et al., 2005; Zachariadis and

Pashourtidou, 2007; Asadoorian et al., 2008; Bessec and Fouquau, 2008; Vassileva et al., 2012;

Ahmed et al., 2012). In other words, the effect of climate on electricity demand depends largely

on the main use of electricity, as influenced by various weather characteristics (Lam et al., 2008).

Although temperature is widely known to be highly correlated with electricity consumption, it is

not the only climatic variable considered in the literature. Sailor and Muñoz (1997); Yan (1998);

Valor et al. (2001); Hor et al. (2005); Hekkenberg et al. (2009); Apadula et al. (2012); Tung et al.

(2013) include temperature data along with other weather variables such as relative humidity,

wind speed, cloud cover, and solar radiation to evaluate the impact of climate on electricity

consumption. They conclude that temperature is the most significant climatic factor.

1.3 Data Description & Summary Statistics

The primary dataset used in this study was provided by HECO. The dataset was made available

to the University of Hawaiʻi Research Organization (UHERO) under a confidentiality agreement.

Covering a period from September 2010 to May 2014, the data contains measurements of net

electricity load, solar PV capacity installed, a number of customers on each rate schedule, and a

variety of weather variables including average temperature, relative humidity, average wind

speed and solar irradiance for 115 distribution transformers on Oahu, Hawaiʻi.

5

For the purpose of this study, electricity net load is defined to be the amount of energy met by

utility generation, while electricity gross load corresponds to the total demand, or total electricity

used, by customers. Electricity gross load is met by a combination of electricity provided by the

utility and electricity produced by local distributed generations such as wind and rooftop PV

systems. The difference between net and gross load is, therefore, the amount of electricity

produced by distributed generations. Without the precise measure of behind-the-meter solar

output, gross load or the total electricity demand is rather difficult to accurately estimate. As a

result, we will limit the focus of our study to the impact of increased PV penetration on net

electricity load.

Table A.1 provides summary statistics of variables used in this analysis at a transformer level.

The net load data analyzed in this paper consists of load measurements taken every 15 minutes,

corresponding to a total of 96 daily recorded values, and covering the period from September

2010 to May 2014. Using this data, the representative daily load set for different months and

years in the study period can be derived. For every month, the net load values recorded at a given

time of day (e.g., 2:15 or 14:45 hours) are used to calculate the standard deviation (SD) for each

of the 96 daily time periods. For example, the SD of all load values recorded at the hour of 12:30

from June 1, 2011 through June 30, 2011 are used to calculate the overall SD at the hour of

12:30 for the month of June 2011. These SD values are considered to be representative load

variabilities for the given month. Table A.1 shows standard deviation of net load ranges from 3.1

kW to 1800.5 kW with the mean of 270.9 kW.5

The standard deviation of net load calculated for each 15-minute period captures the volatility of

“net” electricity consumption. The shape of a given areas’ load profile is most influenced by its

customer-mix and the time-of-day, while its load volatility is largely the result of weather

patterns and the level of PV penetration. We describe summary statistics and how we calculate

these variables in the following sections.

1.3.1 Time-of-Day & Customer Mix

The sample data covers 115 distribution transformers servicing 199,704 distinct customers.

Table A.1 shows summary statistics of the number of residential and commercial customers on

5 Outliers and errors are eliminated by checking daily load graphs. We deleted the whole day that contains errors or

outliers. Holidays are also excluded.

6

each transformer. Of the 199,704 total customers contained within the dataset, 21,381 are

classified as commercial while the remaining 178,323 are classified as residential. The customer

classification is based on their rate schedules.6 The number of customers on a single transformer

ranges between 45 and 5,459 depending on the location where the distribution transformer

supplies power to. Although the number of customers significantly differs across areas and varies

over time, the data on the number of customers in this study stays constant across time, due to

the limited availability of historical information. We use the data on the total number of

customers and customers on residential rate schedule to calculate the percentage of residential to

total customers within each area, which ranges from 0% to 99% and averages 79%.

Time-of-Day

Table A.2 extends summary statistics for the standard deviation of net load by time-of-day,

season and year. It is observed that the statistics of net load is higher during the day and

increasing year-over-year. As expected, the average of net load volatility is greater during the

day due to both the consumption behavior of customers and the nature of intermittent solar

power generated by rooftop PV. An increase in average net load variations over the years

suggests that increasing penetration of PV makes net load more volatile. Between each season,

however, net load volatility behaves very similarly.

Customer Mix

Different transformers in our data set are observed to exhibit a variety of shapes and load profile

patterns. Figures B.2, B.3, and B.4 illustrate representative daily load patterns during each year

for three different customer-mixes with relatively high percentage of PV penetration. These

figures depict both the annual average net load profile (black solid line) and the load volatility

(green band represents the maximum and minimum values) throughout the day, and the annual

kilowatt (kW) PV installed capacity (solid red line). It is observed that customer-mix exerts a

significant impact on the pattern and level of net load from hour-to-hour.

6 Note that HECO currently does not have a separate category for industrial customers. Particularly, customers are

classified into two main types: residential and commercial. Commercial customers are further subdivided into three

major classes: small, medium, and large commercial dependent upon the magnitude of their electricity use. In this

paper, we use the detail of customer information on each transformer to determine whether customers are industrial

or commercial.

7

Figure B.2 is an example of a residential concentrated area. This transformer consists of 99%

residential households and only a few small commercial customers. When examining the annual

average net load in 2011 (solid black line), two distinct peaks are noted. The first peak

corresponds to morning (5:00 am - 7:00 am) and the second peak to evening (6:00 pm - 8:00

pm). This pattern can be attributed to residents waking up in the morning and later returning

following a day at work or school. Between the peaks, the net load is observed to fall during the

midday when the majority of customers are outside of their homes.

Figures B.3 and B.4 show representative annual average daily net load profiles for commercial-

and industrial-concentrated areas between 2011 and 2014, respectively. Commercial and

industrial load profiles often display similarities depending on the type of commercial and

industrial customers on the transformers. In 2011, before large gains had been made in solar PV

adoption, both load profiles exhibited a midday peak corresponding to regular business hours,

which gradually decreased towards a nighttime low as the majority of businesses closed for the

day. Although the representative commercial transformer captured in figure B.3 is comprised

only of 19% commercial customers, they are majority medium and large commercial users.7

Conversely, the industrial-concentrated population in figure B.4 consists of 100% commercial

and industrial customers.

Although the load profiles for commercial- and industrial-concentrated areas exhibit similar

patterns during weekdays, they are found to diverge from one another during the weekend.

Figure B.5, which displays 7-day net load profiles from August 28, 2011 to September 3, 2011,

illustrates the difference in load patterns between the three primary customer-mixes transformers.

It is observed that the load profile of the sample commercial-concentrated transformer is largely

uniform throughout the week, with little deviation between weekdays and weekends.

Conversely, the industrial-concentrated transformer exhibits divergent load profiles between

weekdays and weekends. Weekday load profiles of industrial-concentrated transformers typically

mimic those of commercial-concentrated ones, exhibiting a midday peak followed by a nighttime

lull. However, average weekend loads are observed to remain flat at minimum usage levels. This

7 Note that medium and large commercial customers consume 28.9% and 41.6% of the total annual electricity

consumption on Oahu. Since these commercial customers draw a large amount of electricity on this transformer,

having only 19% of commercial customers is sufficient to convey a representative commercial load profile.

8

pattern can be attributed to the fact that industrial customers do not typically operate during

weekends, although certain machines and/or electrical appliances may remain on when

businesses are closed. This differs from weekend loads of commercial-concentrated areas where

commercial customers such as groceries and department stores remain open throughout the

weekend, leading to load profiles that exhibit little variation over the course of a typical week.

Several studies Apadula et al. (2012); Hekkenberg et al. (2009); Pardo et al. (2002); Moral-

Carcedo and Vicens-Otero (2005) have shown that daily electricity demand is strongly

influenced by calendar effects, repeated sequences of weekdays and weekends which constitute

underlying periodic 7-day trends. These weekly cycles are among the main drivers of short-term

variations in electricity use. The recurring trend of higher electricity consumption during

weekdays is common to industrial-concentrated areas. Electricity consumption patterns of

residential households, wherein midday consumption is higher on weekends when a majority of

households are home, are also displayed in figure B.5.

1.3.2 Weather Variations & Solar PV Penetration

Weather data from a variety of sources is leveraged in support of this study. Weather variables

are estimated by averaging 15-minute time intervals in the same manner as was used for net load

data. Measurements of air temperature, relative humidity, and average wind speed were recorded

by weather sensors installed in several different areas on the island of Oahu. Weather variables

were queried on the basis of their relative geographic location to transformers and in the form of

power per unit area. Average temperature and relative humidity data were gathered by sensors at

four distinct locations on Oahu. By matching each transformer to its closest sensor, an estimate

of weather variations in each area may be attained. Average wind speed data was sourced from

two wind farms located on the northern coast of Oahu and is assumed to be identical for all

transformers in the study.

A number of other studies employed temperature-derived variables such as cooling (CDD) and

heating degree-days (HDD) when examining the impact of weather on electricity demand (Valor

et al., 2001; Hor et al., 2005; Amato et al., 2005; Moral-Carcedo and Vicens-Otero, 2005;

Zachariadis and Pashourtidou, 2007; Ahmed et al., 2012; Blázquez et al., 2013). Other studies

elected to exploit a wide combination of weather variables including temperature, humidity,

wind speed, cloud cover, rainfall, and solar radiation. (Engle et al., 1986; Filippini, 1995; Henley

9

and Peirson, 1997; Sailor and Muñoz, 1997; Yan, 1998; Henley and Peirson, 1998; Considine,

2000; Valor et al., 2001; Pardo et al., 2002).

In this study, a number of climatic variables are utilized to better understand the effect of

weather on the volatility of electricity load. Climatic variables were used in lieu of CDD/HDD as

an indicator of weather variability in this paper for a number of reasons. First, HDD data are

always zero in Oahu, Hawaiʻi. Although monthly CDD data are non-zero, the use of more

granular data is better than the use of a daily measurement of CDD. Leading to a second

justification, the frequency of our weather data is at the 15-minute time interval. The higher

frequency of our variables in the data set enhances the analysis at each 15 minute.

Temperature

Hawaiʻi exhibits considerably less temperature variation compared to other states. From table

A.1, the mean average temperature is 24.36 degrees Celsius with a standard deviation of 3.11

degrees. The highest and lowest average temperatures were observed in September and February,

respectively.

Relative Humidity

Relative humidity is a measure of moisture in the air which plays an important role in how

people perceive temperature.8 Sweat evaporates easily when the relative humidity is low, cooling

the body. Conversely, when relative humidity is high, sweat evaporates less readily leading to

higher perceived temperatures. At the extreme, when relative humidity reaches 100%, sweat no

longer evaporates into the air.9 The effect of both air temperature and humidity plays a major

role in a person’s likelihood to utilize air conditioning. Given the relatively small variations in

temperature experienced in Hawaiʻi, the additional consideration of humidity provides a better

understanding of how customers perceive and respond to different air temperature values.

The summary statistics of relative humidity are shown in table A.1 with a mean of 71.19% and a

standard deviation of 9.59%. The highest relative humidity during the study period was recorded

8 Relative humidity is a percentage of the maximum amount of water vapor that the air could hold at a given

temperature. 100% relative humidity implies that the air is totally saturated with water vapor and cannot hold

anymore, creating the possibility of rain. However, the relative humidity near the ground is generally much less than

100%. 9 For example, if the air temperature is 25 degree Celsius and the relative humidity is 0%, the air temperature feels

like 22 degree Celsius to our bodies. But when the relative humidity is 100%, we feel like it is 28 degree Celsius.

10

in August where the lowest was in January. Figure B.6 depicts a negative relationship between

average temperature and humidity, whereby humidity is lower when the temperature is high.

This negative relationship is most pronounced when solar is greater than zero (orange dots),

particularly during periods of high sunlight. This is intuitive given that sunlight reduces water

vapor in the air, lowering humidity and increasing temperature.

Wind Speed

Recorded average wind speed ranges from 3 to 13 miles per hour (mph), with a mean of 7.79

mph and a standard deviation of 2.59 mph. The highest and lowest average wind speeds typically

occurred during the months of July and January, respectively. Wind patterns on Hawaiʻi are

strongly influenced by the trade winds. Average wind speed is estimated for 15-minute time

intervals from data recorded at two different wind farms located on the northern coast of Oahu.

Given the limited number of wind speed sensors, there is considerably less variation in wind

speed data among transformers in the sample.

Solar Irradiance

Solar irradiance is a measure of power per unit area produced by the sun in the form of

electromagnetic radiation. Solar irradiance data in this study was calculated from PV power

output provided by anonymous customers with rooftop PV systems. Each customer is first

mapped to a transformer on the basis of their geographic location. The average solar power

produced by residential rooftop PV systems within each area is calculated in order to construct

an overall solar profile. This study utilizes a normalized measure of solar irradiance with values

falling between 0 and 1. Solar irradiance was found to range between 0 and 0.89, with an average

of 0.19 and a standard deviation of 0.26 (see table A.1). Figure B.7 illustrates a similar pattern of

average solar irradiance in winter and summer months at each time period throughout the day.

PV Penetration Level

The percentage of PV penetration reflects the percentage of daytime minimum electricity

consumption on a transformer that is covered and/or generated by local rooftop PV systems. In

this study, we employ percentage of PV penetration as a proxy for the amount of solar saturation

on each transformer. It can be calculated as follows:

11

% of PV Penetration = PV Installed Capacity (kW) x 100 (1.1)

Daytime Minimum Load (kVA)

where daytime minimum load (DML) represents the minimum load for a given location during

daytime (9:00 am to 5:00 pm). We calculate the value of DML of each transformer by first

matching each individual distribution circuit to their corresponding transformer.10 The DML of

each circuit under a given transformer is then summed to determine the DML at the transformer

level. Table A.1 shows that DML ranges between 108 and 4,412.2 kVA with a mean of 2,230.39

and a standard deviation of 896.05. The dataset detailing the amount of solar PV capacity

installed on each transformer was provided by HECO. It consists only of those PV customers

with executed agreements.11 The dataset provides details on solar system size, or PV nameplate

capacity, along with the date of installation.

The electricity load of each distribution transformer not only behaves differently throughout the

course of the day but also changes dramatically as solar PV penetration rises. In the sample

residential transformer shown in figure B.2, a clear decrease in daytime net load is observed

from 2011 to 2014. This is due in large part to a significant increase in the level of PV

penetration. In 2011, when the number of PV installations was relatively low, the annual net load

profile showed an increasing load during the midday with a nighttime peak. By 2012, following

an increase in PV installations, the midday load had dropped while simultaneously

demonstrating higher volatility during daytime hours when the sun was out and solar power was

readily available. Beginning in 2014, a back-feed problem on the residential-concentrated

transformer is observed, with the minimum net load declining below zero. During daytime hours,

the combination of lower residential power demand and higher electricity generated from rooftop

PV causes the net load profile to drop substantially. The nighttime peak does not, however,

exhibit the same degree of change over the study period. This implies that the nighttime behavior

of residential consumers remained largely unchanged despite the rise in PV installation.

10 Each distribution transformer in this study consists of one to four distribution circuits depending on the number of

customers, their relative location, and grid infrastructure. 11 These agreements include PV customers under Net Energy Metering, Feed-in Tariff, and Standard

Interconnection Agreement.

12

In addition, it can be clearly observed that in figure B.2 the midday sag in residential energy

demand becomes more pronounced from 2011 to 2014 as rooftop PV energy generation exceeds

energy demand. During this time period, the midday variation is also observed to increase. The

steep curve following the midday low rises as solar energy diminishes and late afternoon

consumption rises. There is a marked disruption attributable to PV generation, which causes net

load to behave differently than before. Due to this, the utility is confronted with a situation

wherein it must turn down its generators when solar reaches its peak, and then later ramp them

up more quickly than usual when solar power availability declines in the evening.

Figure B.4, a representative industrial-concentrated transformer, displays a dramatic decrease in

daytime net load. As discussed earlier, industrial customers typically use less electricity on

weekends when businesses are closed. The lower band, representing the minimum net load is

observed to drop below zero starting in 2012 due to a sharp increase in the number of solar PV

installations. The variation in net load increases over the course of the study period due to excess

electricity generated by rooftop PV, especially during weekends when demand is at its minimum.

This back-feeding during weekends lowers the average net load on the transformer over time.

1.4 Methodology

In line with the availability and description of our data in the previous section, we employ a fixed

effects model, which controls for time-of-day, month and year effects, and a set of covariates.

Our goal is to capture the effect of relevant variables on net load volatility. We hypothesize that

the volatility of net electricity load at time t for each distribution transformer i depends on the

level of PV penetration, the mix of customer classes, weather variations, time-of-day and

seasonal variations.

Y = f(PV Penetrationit, Customer Mixi, Weatherit, Time-of-Dayt, Seasonal Trendt) (1.2)

The dependent variable in our analysis is the logarithm of standard deviation of electricity net

load. We further employ a number of meaningful interaction effects which greatly enhance

understanding of the relationships among variables in our analysis.

13

In the baseline model, we evaluate the impact of potential drivers of changes in net load

volatility. These drivers include a percentage of PV penetration, weather variables, and time

dummies.12

ln(SDNLit) = β0 + β1ln(PVPenit) + β2Tempit + β3Humit + β4SIit + β5Windit (1.3)

+ β6DNdum + β7SWdum + γTD + it

where lnSDNLit is the standard deviation of net load on a transformer i at time t. Note that since

the variables in our model are measured at every 15 minute and vary from month to month and

year to year, our time component (t) represents the time of day in each month and on each year.

For example, the average temperature at noon on January 15th, 2013 is different from that of the

same date in 2014. lnPVPenit denotes the percentage of PV penetration in logarithm value on a

transformer i at time t. The coefficient on lnPVPenit (β1) gives a PV penetration elasticity of net

load volatility. In order to estimate the effect of weather variations, we include Tempit, Humit,

SIit, and Windit which are average temperature in degree Celsius, average percentage relative

humidity, average solar irradiance, and average wind speed in mile per hour on a transformer i at

time t, respectively. DNdum is a day/night dummy variable defined to be 1 for daytime (9:00am -

5:00pm) and 0 for nighttime (5:15pm - 8:45am). SWdum is a season dummy – equals 1 for

summer (May to October) and 0 for winter (November to April). TD denotes a vector of time

dummies: time, month and year dummy variables. We estimate the baseline equation (1.3) using

fixed-effects estimator.

Next, to capture the impact of customer diversity and increased solar penetration on net load

variation, we employ the first interaction term into our baseline equation (1.3):


+ β6DNdum + β7SWdum + β8RPVit + γTD + ρit

where RPVit is the interaction effect between the percentage of residential customers and log of

PV penetration. Since the percentage of residential is time-invariant in this analysis, we omit its

main effect in our fixed-effects model. As mentioned in the previous section, the shape of net

12 We apply log transformation on both standard deviation of net load and percentage of PV penetration to make

them normally distributed.

14

load profiles is greatly influenced by the mix of customers on each area, incorporating this

interaction term (RPVit) will entail the impact of increased PV penetration on the volatility of net

load conditional on various values of customer mix. With the interaction term RPVit, the

coefficient on lnPVPenit (β1) in equation (1.3) changes its meaning. In equation (1.4), significant

β1 entails the main effect of PV penetration on net load volatility when the percentage of

residential customers equal zero. That is, for example, a negative and significant β1 would imply

that as PV penetration increases variation of net load decreases when a transformer is fully

commercial- or industrial-concentrated.

The second interaction effect is employed to assess the impact of increased PV penetration on

net electricity load variation conditional on the intermittency of solar resource.


+ β6DNdum + β7SWdum + β9SIPVit + γTD + it

where SIPVit denotes the interaction effect between average solar irradiance measure and log of

PV penetration. The interaction effect in equation (1.5) conveys the impact of increased solar

penetration on net load volatility depending on the fluctuation in solar resource. Since adding an

interaction effect changes the interpretation of all the relevant coefficients, β1 in equation (1.5) is

now interpreted as the effect of PV penetration on net load volatility when solar irradiance equals

zero. That is, if β1 is insignificant, then increased in percentage of PV penetration has no impact

on changes in net load at nighttime. Likewise, β4 is now the effect of solar resource on net load

volatility when percentage of PV penetration equals zero.

Lastly, we further explore the impact of weather variations on net load volatility by including an

interaction effect between temperature and humidity.


+ β6DNdum + β7SWdum + β10TempHumit + γTD + αit

where TempHumit is the interaction term between temperature and humidity. As mentioned in the

previous section, with the relatively small variations in temperature in Hawaiʻi, the level of

15

humidity in the air can make it feel hotter or cooler. This interaction effect is used to capture the

impact of both temperature and humidity on fluctuations in net load.

1.5 Empirical Results

Results of several specifications are reported in table A.3. In addition to the models specified in

the previous section, we include models of two or more interaction terms to capture the effects of

explanatory variables. Column (1) in table A.3 reports regression results of our baseline model

(1.3) without interaction terms. The PV penetration elasticity of volatility of net electricity load

is positive and statistically significant at 5%. The predicted coefficient implies that if the level of

PV penetration in a certain area were to increase by 100%, the volatility of net electricity load on

that transformer would be expected to increase by 3%, ceteris paribus.

The estimated coefficients for average temperature and wind speed are both found to be

statistically significant at 1%. The average temperature has a positive effect on net load volatility

with a 1 °C increase in average temperature increasing the volatility by 5.2%, holding other

variables constant. The fluctuation in electricity demand by households when temperatures are

high, resulting from increased use of air conditioning, for example, creates instability in

electricity use. Conversely, lower temperatures result in a more balanced net electricity load

throughout the day due to a decreased inclination to turn on fans or air conditioning.

The estimated coefficient of wind speed is equal to -0.018 and found to be statistically significant

in all specifications. For every one mile per hour increase in average wind speed, the volatility of

net load is predicated to decrease by 1.8%. Higher and sustained wind speed makes the weather

slightly cooler reducing the need to switch on and off cooling appliances.

Both dummy variables, day/night and summer/winter dummy, are significant at 1%. The positive

coefficient on the day/night dummy variable suggests that net load volatility is higher during the

day than during the evening. This result is clearly shown in figure B.8 which depicts higher

distributions in net load volatility during the daytime. The results in column (1) in table A.3 also

indicate that the volatility of net electricity load is lower during the summer than during the

winter months. Since it is generally sunnier and hotter in the summer, net electricity load is more

consistent and less variable.

16

Column (2) in table A.3 illustrates the impact of customer mix and PV penetration on load

volatility. The coefficient of the interaction term is positive and statistically significant, while the

coefficient of the log of PV penetration is negative and statistically significant. This indicates

that higher PV penetration increases the volatility of net load in residential-concentrated areas

while reducing the volatility in commercial- and industrial-concentrated areas.

Figure B.9 displays annual net load profiles of four different transformers with comparable PV

penetration levels.13 Figure B.9a and figure B.9b depict patterns similar to those observed in

figure B.2 and figure B.3, having slightly lower variation in daytime load due to lower levels of

PV penetration. When comparing figure B.9c and figure B.4, it is observed that figure B.9c

exhibits smaller minimum and higher average net load during the day. This difference is due

primarily to the impact of excess power generation on weekends, as the transformer in figure

B.9c has a smaller number of behind-the-meter rooftop PV installations.

Figure B.9d illustrates the annual net load profile of a transformer consisting of a mixture of

residential and commercial customers (77% residential with several medium-sized commercial

businesses). The average net load of this transformer drops marginally during the daytime,

altering the shape of the load curve. As before, the daytime variability in net load is observed to

have increased over time. However, this increase is less pronounced than was seen in more

residential-concentrated (figure B.9a), commercial-concentrated (figure B.9b) or industrial-

concentrated areas (figure B.9c). Again, it is clearly observable that customer-mix is a key factor

influencing net load behavior in each area. During daytime hours, excess electricity generated by

rooftop solar PV systems is in turn used by the transformer’s commercial customers. The

dynamic between residential and commercial demand patterns greatly reduces back-feeding and

other issues resulting from high variability in net load.

Several existing studies have attempted to determine how heterogeneity in consumer

characteristics and behaviors affect electricity consumption patterns using disaggregated data

Espinoza et al. (2005); Verdú et al. (2006); Lam et al. (2008); Widén and Wäckelgård (2010);

13 These 4 sample transformers have less PV penetration level than figure B.2, B.3, and B.4. Figure B.9a consists of

98% residential customers while figure B.9b comprises only 2% residential customers with two large commercial

businesses. The majority of customers in the transformer in figure B.9c are commercial with two large industrial

businesses and only 4% residential consumers. Figure B.9d consists of a good mix of residential and commercial

with percentage of residential to total equals 77%.

17

Chicco (2012); Flath et al. (2012); Vassileva et al. (2012); Yang et al. (2013); Albert and

Rajagopal (2013). Electric utilities are responsible for supplying power to a wide variety of

different customers. It has been found that electricity consumption patterns are generally similar

within a customer class while differing between classes (Chow et al. 2005). Our results,

therefore, suggest that it is vital for utilities to distinguish load behavior of each customer class

separately, especially when taking into account the impact of a rapid flux in distributed

generations as seen with rooftop PV systems. Understanding the load patterns characterizing

each customer class is of great value to a utility, not only enhancing their ability to better

distribute power generation, but also targeting consumers with appropriate incentive programs.

Column (3) in table A.3 includes the interaction effect of PV penetration and the fluctuation of

solar resource. The main effect of solar irradiance is negative and statistically significant,

implying that when PV penetration is at 0%, as solar irradiance increases the variation in net load

decreases. The coefficient estimate on log of PV penetration becomes insignificant in this

specification, indicating that PV penetration has no effect on the grid at nighttime. The positive

coefficient on the interaction term between log of PV penetration and solar irradiance, however,

suggests that conditional on the level of PV penetration, net load becomes less fluctuating when

it is sunny and there is less cloud in the sky. Given high levels of PV penetration, higher solar

irradiance implies that rooftop PV systems generate higher and more consistent power output

which then results in less variation in net electricity load.

Column (4) in table A.3 provides estimates of the interaction term between temperature and

humidity. The negative coefficient on the interaction term suggests that when humidity is high,

increasing temperatures still result in an increase in volatility of net electricity load, albeit at a

diminishing rate. For example, an increase in temperature from 28 °C to 30 °C will have a

smaller impact on people’s electricity consumption decisions when humidity is already high.

Intuitively, this can be attributed to the fact that most consumers will have already turned on

their air condition when the temperature was at 28 °C.

1.5.1 Additional Result

To capture the effect of a rapid increase in solar penetration, we further evaluate the same

analysis using data only on daytime period (9:00 am to 5:00 pm). Table A.4 reports regression

results from the daytime analysis. From the baseline model, the coefficient on log of PV

18

penetration in column (1) in table A.4 is much greater in magnitude comparing to the same effect

in table A.3. When we consider only daytime, a 100% increase in PV penetration leads to a 9.5%

increase in net load volatility. The positive effect of temperature on net load variation, on the

other hand, decreases from 5.2% to 2.2% with a 1 °C increase in average temperature. The

diversity of customer types on an area also has a greater impact on net load volatility as shown in

column (2).

1.6 Conclusion & Discussion

The unprecedented growth in solar PV adoptions over the past few years has resulted in

remarkably high levels of PV penetration in Oahu, Hawaiʻi. Given this rapid increase in PV

installations, along with the intermittent nature of solar resource itself, the ability to integrate a

vast amount of behind-the-meter rooftop PV systems into the grid has become a costly and

perplexing proposition. This study endeavors to address the underlying determinants of

variability within net electricity load, specifically in light of increasing levels of solar saturation

in Oahu.

Using standard deviation of electricity net load as representative of load volatility, we find that

net load becomes increasingly more volatile as the percentage of PV penetration rises. This

impact, however, is not present at nighttime, implying that consumption behavior of electricity

consumers may remain unaffected by the rapid growth in PV installations. We further assess the

impact of customer diversity on net load volatility and find that customer mix is the key driver

affecting the behavior of electricity net load on each distribution transformer. With an

accelerated increase in solar penetration, the dynamic of electricity consumption behavior

between different types of consumers can essentially lessen problems following higher

fluctuations in electricity net load resulting from variability in solar power output.

From the utility perspective, understanding how net load changes following the rapid increase in

PV installations is crucial. With a more disaggregated data set, electricity consumption patterns

can be used to assess related policies and identify better pricing structures. Finally, the utility can

reduce costs associated with integrating more behind-the-meter solar systems into the electric

grid by fashioning appropriate incentive programs to attract the optimal mix of consumers.

19

CHAPTER 2

Evolution of Residential Solar Adoption in Oahu, Hawaiʻi

2.1 Introduction

Innovation diffusion theory studies the stages underlying the adoption of innovations, the process

of adoption decision-making, and the characteristics of adopters (Rogers 2010). Perception of a

technology, generally based on the characteristics of that technology and people’s level of

awareness, plays an essential role in adoption decisions and, by implication, affects the speed of

diffusion. The awareness stage in the innovation-decision process represents the point at which

adopters gain a full understanding of a technologies’ attributes, and are therefore able to progress

to the decision-making stage. Innovation diffusion is facilitated through various communication

networks over time, influencing the rate of adoption, the innovation decision process, attributes

of new technologies, and the role of change agents. Rogers (2010) divides adopters into five

categories on the basis of their behavior, attitudes, values, personality and the timing of adoption.

These categories are: innovators (2.5% of adopters); early adopters (12.5% of adopters), early

majority (35% of adopters); late majority (35% of adopters); and laggards (15% of adopters).

Under Roger’s classification of adopters, Hawaiʻi households with solar photovoltaic (PV) may

be best categorized as either innovators or early adopters. However, given the rapid evolution of

the Hawaiʻi PV market, which presently has the highest PV penetration rate in the nation, one

might surmise that Hawaiʻi is progressing past the early adopter phase.14 Hawaiʻi, therefore,

serves as a case study for other states presently lagging behind it in the rate of solar adoption. As

the rate of solar adoption increases in other states, Hawaiʻi’s experiences will provide valuable

insight into the unique barriers and challenges inhibiting PV uptake. It is therefore vital that we

gain a better understanding of the adoption process for solar technology, and how it is evolving

over time.

The primary objective of this study is to examine adoption trends and characteristics of PV

adopters on Oahu, Hawaiʻi. We describe both the general attributes characterizing PV adopters

14 As of January 2016, 17% of Oahu customers have had PV installed and 32% of single-family homes on Oahu

have installed solar PV.

20

and the evolution of solar installation trends over the years. By quantifying the various factors

influencing consumers’ solar PV adoption decisions, one is able to improve the efficacy of solar-

related incentives and policies.

Identification of characteristics differentiating PV from non-PV households is done using

detailed information on the time of installation, enabling one to observe the evolution of PV

adopters over time. Homes having PV installations were found to be newer, larger, more energy

efficient, and less costly per square foot than those without a PV installation. The analysis also

revealed that early PV adopters, defined as those installing PV systems before 2012, were

generally older, wealthier, more likely to own their own home, and had higher levels of

educational attainment than did their contemporary counterparts.

To investigate the likelihood of solar adoption among residential single-family households, a

logistic regression model incorporating household consumption level, solar resource availability,

and demographic and housing characteristic information was developed. Empirical results

derived from this model align with descriptive evidence, demonstrating that those living in

larger, newer and less expensive (on a square foot basis) homes were more likely to install solar

PV. Based on demographic information at a census block group level, we find that areas with a

smaller household size, lower median age, higher levels of education, and higher median income

were more likely to have significant solar PV adoption.

The remainder of the paper is organized as follows. Section 2.2 reviews literature related to this

study. Section 2.3 introduces the proprietary dataset underlying the presented analysis and

describes how each variable was processed and summary statistics were developed. Section 2.4

presents descriptive evidence for the data. Section 2.5 details the econometric methodology used

in the analysis, with estimation results reported in Section 2.6. Finally, Section 2.7 offers

concluding remarks and additional discussion of the results.


There exists a growing body of literature examining the influence of socioeconomic and

customer characteristics and upon the likelihood of solar PV adoption (Keirstead 2007; Rothfield

2010; Kwan 2012; Mills and Schleich 2012; Rai and McAndrews 2012; Balcombe et al. 2013;

Rai and Sigrin, 2013; Langheim et al., 2014; Chernyakhovskiy 2015; Graziano and Gillingham

21

2015). Utilizing zip code level data, Kwan (2012), analyzes the link between a variety of factors

and the distribution of residential solar PV installation. The author found that the level of

available solar resource was the most important factor influencing residential installation, with

higher levels of solar insolation corresponding with increased PV penetration. Other factors

exerting a positive influence on PV adoption include electricity prices, the availability of

financial incentives, and median home values. The paper concluded that the likelihood of PV

adoption was highest among certain groups – namely college educated individuals between 25

and 55 years old with a median income between $25,000 and $100,000 a year.

A number of other studies have employed disaggregated household-level data to identify the

relationship between household characteristics and solar PV adoption. Keirstead (2007), utilizing

demographic information captured in questionnaire response of 91 PV households in the UK,

found that income, education, and homeownership were the primary predictors of solar adoption.

A similar study by Rai and McAndrews (2012) analyzed the socio-demographics of 365 PV

households in Texas using data obtained via a household survey. The survey results found that

residential PV adopters had higher income levels, and were more highly educated than the

average Texas resident.

Although these prior studies assessed the influence of demographics and housing characteristics

on residential solar PV adoption, they failed to analyze the evolution of solar adoption trends

over time. Moreover, their conclusions were based on relatively small samples, which offered no

comparison between PV and non-PV households. The present study aims to fill this literature

gap by analyzing the evolution of PV and non-PV household demographics in order to determine

whether the prototypical solar household has changed over time.

2.3 Data Summary

2.3.1 Data sources

Consumption and PV Installation

Data used in this study were gathered from several different sources. The first dataset consists of

proprietary billing information for 4,047 residential customers covering the period from January

2000 to May 2016. It was made available to the University of Hawaiʻi Research Organization

22

(UHERO) under a confidentiality agreement with Hawaiian Electric Company (HECO), the sole

electric utility on Oahu. The sample was generated by randomly selecting customers using a

random sampling procedure which is explained in detail in Appendix E. Of these customers,

2,490 installed solar PV systems under the Net Energy Metering (NEM) program between

February 2003 and May 2016.

Energy usage metrics and customer information, derived from two ancillary sources, were joined

on the basis of customer installation numbers to form the overall dataset. The first component

dataset contained monthly electricity consumption data in kilowatt-hours (kWh), account and

meter numbers, and meter read dates. Billing data for non-PV customers consisted of actual

monthly electricity consumption. For PV customers, electricity consumption was calculated as

the difference between the amount of electricity delivered from the grid, and the excess

electricity generated by rooftop solar and exported back to the grid by the customer. The second

dataset contained service address, electric distribution zone, an indicator for whether a household

had a solar hot water heater installed, and solar PV installation information (PV system capacity

in kilowatts (kW) and date of installation).

Solar Irradiance

The second dataset, created from two ancillary sources, consists of monthly global horizontal

solar irradiance data (GHI) in Watt/m2 (W/m2).15 The first source, which was provided by AWS

Truepower, LLC and HECO, contains detailed GHI data from over 900 gridded

latitude/longitude points across the island of Oahu. The GHI data points cover the period from

January 2013 through May 2016. The second source was drawn from Clean Power Research’s

SolarAnywhere® PV Power Map and covers the period between 2001 and 2013. It includes

hourly GHI data on a 10-by-10 kilometer (km) tile. For the purposes of this study, 20 tiles

encompassing different parts of Oahu were analyzed.

Housing Characteristics

The third dataset contains housing characteristics, Tax Map Key (TMK) separation, and building

permit information. Housing metadata was obtained from the Real Property Assessment

Division, Department of Budget and Fiscal Services, City and County of Honolulu. For each

15 Global Horizontal Irradiance (GHI) is the solar insolation received by a fixed flat horizontal surface, representing

in the unit of W/m2.

23

household in the sample, the dataset provides information on total property assessed value ($),

types of housing occupancy (single-family and apartment), dwelling size in square footage (sqft),

year built, and number of bedrooms, bathrooms and half-baths. The TMK separation and

building permit details were gathered from the Department of Planning and Permitting (DPP)

and consist of census tract, census block group (CBG), and the total accepted value of solar PV

installations ($) for customers with solar PV.

Census Details

The fourth and final dataset consists of census information obtained from the American

Community Survey (ACS). It includes data elements reported at the CBG level including an

average household size of occupied housing units, a percentage of population 25 years and over

having a college degree or higher, a percentage of owner-occupied homes, median income ($)

and median age.

2.3.2 Data Processing

The aforementioned datasets required considerable manipulation before they could be leveraged

in our analysis. The ensuing section provides a summary of how these datasets were merged and

filtered prior to analysis.

The consumption and PV installation dataset initially contained records for 5,500 residential

customers. Using customer service address information as a key, data elements pertaining to

housing characteristics and building permit information were joined to create a complete

customer information dataset. While generating this dataset it was decided that certain customer

accounts should be excluded should they meet any of the following conditions:

customers for which the name on the property and the HECO account did not match;

customers who had no property information on the Real Property Assessment Division

website; or

customers whose PV statuses under their HECO account and DPP did not match (e.g.,

customers appearing to have solar installation information on DPP but who were not

classified as PV customers within the HECO database).

A total of 695 customers were excluded from the final population based on the above criteria.

24

Next, households residing in apartment buildings were identified using types of housing

occupancy data. It was discovered that 750 households in the initial sample dataset resided in

apartment buildings without solar PV. After excluding these households from the sample, there

were 4,055 residential single-family households remaining in the sample dataset.

Meter read dates were used to determine the month and year for which billing data were to apply.

The logic for this process is as follows: if the meter read date fell between the 1st and 15th of a

given month, then the consumption data reported was assumed to be for the previous month; if

the meter date fell between the 16th and the end of the month, then the consumption data was

assumed to be for that month.

Solar irradiance of PV households in our sample was derived from two distinct data sources. The

estimated monthly solar irradiance for households during the years 2001 to 2012 was sourced

from the publically available SolarAnywhere database, while internal HECO data (AWS) was

utilized for the years 2013 through 2016.

The AWS data covering the latter years in our study consists of measures taken for over 900 1x1

km grid points comprising the island of Oahu. Each household was first assigned the closest

latitude/longitude grid point based on their address using Google Earth as shown in figure D.1.

This mapping produces 216 distinct grid points, for which we query solar irradiance from the

AWS data source. Estimated monthly solar irradiance for the period between 2013 and 2016 was

then determined for each of these grid points, which were subsequently joined to the customer

dataset.

Determination of solar irradiance for the years 2001 through 2012 was performed using hourly

GHI data from the SolarAnywhere dataset. From this data source, we derived total monthly GHI

for each of twenty different tiles which are illustrated in figure D.2. Each customer was then

assigned a tile number (1-20) corresponding to their geographic location.

The SolarAnywhere and AWS datasets overlap in the year 2013. When comparing the values in

each dataset for this overlapping year, we identified inconsistencies between the two measures as

shown in figure D.3. It was, therefore, necessary to adjust the SolarAnywhere observations from

2001-2012 before it was combined with the AWS data in order to achieve a consistent measure

of solar irradiance over the time period considered in the analysis. This was done by first pairing

25

the AWS identifier (1-216) for each household with their corresponding SolarAnywhere tile

number (1-20).

Let AWSit be the estimated monthly solar irradiance of grid point i for month t, while SAit is the

estimated monthly solar irradiance of tile i for month t. Then let AWS-SAit be the estimated

monthly solar irradiance on a combination of the two dataset on a location i at month t. From this

process, we derive distinct 259 grid-tile combinations for customers belonging to our sample

population.

For each of these aforementioned 259 combinations, GHI data is used to calculate an adjustment

factor for each month in the overlapping year (2013) as follows:

AWSit = SAit*it (2.1)

where it is an adjustment factor of a combination i at month t. An overall adjustment factor, i, is

then calculated as the average of these 12 monthly adjustment factors. This overall adjustment

factor is then used to scale SolarAnywhere GHI data for the years 2001-2012 to arrive at a

consistent measure of solar irradiance across the study period as follows:

Adjusted-SIit = SAit*i (2.2)

where Adjusted-SIit is the adjusted values of SAit for tile i during month t. Applying this process,

we obtain monthly solar irradiance (W/m2) for each PV household.

For each PV household, we also determine whether additional PV systems had been added to

their accounts during the observed study period. The initial dataset only indicated the total (i.e.,

current) size of PV systems and the date on which the most recent PV system was installed.

Information detailing the number of additional systems, along with their size and date of

installation, was added using HECO’s internal data portal. From this process, we identified 397

PV accounts with at least one additional PV system installed after the initial PV installation.

Lastly, in order to mitigate the presence of measurement error in monthly reported consumption,

an additional eight accounts were excluded from the study sample. Reasons for exclusion

included unexplained spikes in consumption profiles, prolonged periods of inactivity, and

26

negative or near-zero gross consumption. The complete set of criteria governing exclusion of

specific accounts is as follows:

customer accounts whose gross consumption was negative during any of study months;

customer accounts whose information did not report a solar PV installation, although

their net consumption profiles indicated the presence of a system, having negative

measures for certain months; or

customer accounts exhibiting unusual patterns and/or inconsistent data points. The mean

and standard deviation of monthly consumption were calculated for each customer.

Accounts containing data points exceeding three standard deviations from the mean (>3σ

from the mean) were deleted.

Following this exclusion process, 4,047 residential single-family customer accounts were

ultimately selected for use in the study.

2.3.3 Summary Statistics

The final study sample consisted of 4,047 residential single-family households, 2,490 of which

had installed rooftop PV. The first PV system in our sample was installed in February 2003,

while the latest was installed in May 2016. PV capacity of these systems ranges from 0.28 kW to

35.90 kW.

Table C.1 provides details of variable summary statistics along with t-tests assessing whether

each variable statistically and significantly differed between the two customer groups. Household

consumption was calculated using monthly usage from 2000 to 2005, excluding observations

after PV installation. This measure represents the “baseline” consumption of households in the

sample without the modifying effect of solar installation. It is observed in Table C.1 that PV

households consume approximately 7.5% more energy than non-PV households on average. The

t-test results indicate a statistically significant difference in mean electricity consumption

between PV and non-PV households. The mean monthly solar resource available to households

is found to be equivalent for the two groups.

Housing characteristic information was obtained at the household level. Statistically significant

differences in the mean values were observed between PV and non-PV households, results of

27

which are reported in Table C.1. Home value per square foot was found to be higher for non-PV

households. However, on average, PV homes were found to be larger, newer and use less

electricity on a per square foot basis.

Demographic variables captured at the CBG level exhibited slight differences in their means

between the two customer groups. However, these differences were not found to be statistically

significant, except in the case of median household income at a 4.3% significance level. This

result implies that PV households tend to be located in areas with higher median income.

2.4 Descriptive Evidence

2.4.1 Solar Adoption Trend

This section describes the trend of solar adoption by examining how solar technology has

diffused over time based on the year of PV installation. Figure D.4 illustrates the number of PV

installations and cumulative PV capacity installed of households in the sample. It is observed

that 16% of PV households in our sample have installed additional PV systems after the initial

PV installation.16 The size of these additional PV systems ranges from 0.31 to 15.4 kW, while

the size of original PV systems varies from 0.28 to 35.9 kW.

Several factors have driven the rapid growth of solar PV in Hawaiʻi. First, the availability of

Hawaiʻi solar tax credits and solar incentive programs have played a major role in encouraging

widespread PV adoption. Coffman et al. (2016) address the effect of solar subsidies on

residential PV installations, concluding that investment in solar PV is an exceptional idea for

Hawaiʻi’s homeowners. They argue that various incentives have made solar PV affordable to

many customers, resulting in a significant increase in solar PV adoption.

Secondly, total solar PV installation costs have fallen dramatically over time. We show the trend

in average installation cost of PV in our sample and the trend in the U.S. PV module price in

figure D.5.17 Average installation cost of PV for each year is calculated using the total values of

solar installation obtained from DPP. Comparing the prices of PV systems installed before 2008

with those installed after 2013, we see that the total cost of PV installation has dropped by

16 The number of additional PV systems ranges from 1 to 4 systems per customer. 17 Source: Average value of PV modules, U.S. Energy Information Administration.

28

approximately one-half, increasing the affordability of solar PV and its competitiveness with

other energy sources.

Declining installation costs and solar-friendly policies implemented in Hawaiʻi have led to

remarkable growth in both the number of rooftop PV installations and their average system size

as shown in figure D.6. A PV system installed after 2013 would cost approximately 50% less

than an equivalent system installed prior to 2008. This drop in installation costs has incentivized

consumers to install larger PV systems. The increase in system sizes has raised an anecdotal

issue of whether there exists an “over-sizing” trend in PV installation amongst residential

customers (i.e., the system size chosen by some consumers may be larger than required to satisfy

their energy demand). Given established PV penetration limits on each electrical circuit in Oahu,

this “over-sizing” of PV systems serves to accelerate the speed at which PV penetration

thresholds are met, thereby reducing opportunities for solar adoption by other households.

We next calculate each PV customer’s percentage of consumption offset by their PV systems.

Figure D.7, which shows the percentage of energy offset, illustrates that most households that

adopted PV before 2012 sized their PV systems to displace less than 100% of the total energy

that they consumed. In contrast, the majority of households adopting PV after 2012 installed

systems that offset, on average, 100% of household consumption demand. Figure D.7, therefore,

shows that “over-sizing” of residential PV systems is not widespread. Rather, the increase in

average PV system size observed can be thought of as a natural progression from the “under-

sized” systems installed by early adopters. This result is not entirely surprising given the higher

PV installation costs in the past, larger-than-necessary PV systems were likely not financially

optimal for most residential households.

2.4.2 Characteristics of Adopters & Non-Adopters

Despite the unprecedented growth in residential solar adoption in Hawaiʻi over the past decade,

little attention has been given to examining the types of consumers likely to place solar PV on

their homes. As more households adopt solar PV, the demographics and housing attributes of

adopters also change. In this section, we examine differences in both demographics and housing

characteristics of residential PV adopters and non-PV households on Oahu, Hawaiʻi. Using

detailed information on the time of solar installation, we are not only able to identify which

29

factors are most predictive for solar adoption, but whether these factors are changing as the

technology evolves over time.


Age of Homes

Since the ideal location for solar PV is on a home’s rooftop, it is critical to consider the roof’s

age and condition before installing a PV system. More recently built homes are generally less

likely to require roof replacements to accommodate rooftop solar PV. As a result, one would

expect consumers residing in newer homes to be more likely to install rooftop PV systems

relative to those in aging homes. Figure D.8a illustrates that, in Hawaiʻi, the majority of PV

adopters live in newer homes. However, we also find that the homes of early adopters

(installation prior to 2007) are typically older than those of both recent PV adopters and non-PV

customers.

Home Values

Home value per square foot is calculated using total assessed property value and home size.

From figure D.8b, we find that on average PV homes cost less per square foot than non-PV

homes.

Home Size

Larger homes generally have more rooftop space, resulting in an increased likelihood of PV

adoption. This is illustrated in figure D.8c, which shows that the homes of PV adopters are larger

than non-adopters’ homes on average.

Consumption Level

In terms of consumption level, we calculate an average “baseline” electricity consumption of

each household in the sample. As can be seen in Figure D.8d, most households that adopted PV

before 2010 consume less electricity on average than both recent PV adopters and non-PV

adopters. However, the trend of solar adoption has been transitioning towards high consumption

households in recent years.

30

Home Energy Intensity

Given that increased dwelling size is highly correlated with higher levels of electricity

consumption, we calculate an energy intensity index based on household electricity use per

square foot.18 We observe in figure D.8e that the homes of most PV adopters are more energy

efficient than those without PV. This supports finding from previous studies that adoption of

solar PV is correlated with investment in energy efficiency measures (Haas et al. 1999; Dato

2015). In other words, PV households are more energy-conscious and likely to conserve

electricity.

Demographics

Age

Although data limitations restrict our ability to determine the exact age of individual PV

households in the present study, census level data nonetheless provides some insight. In figure

D.9a we see that most households installing PV before 2009 were typically located in areas

having higher median age than non-PV households and recent PV adopters in the sample. A

decreasing trend in the median age of PV adopters can be observed in the figure, implying that

PV adoption has been transitioning towards younger age groups.

Income

Due to the high upfront cost of PV, households with greater disposable income and better credit

capacity are more likely to purchase solar PV. In figure D.9b we find that the majority of

households that adopted solar PV before 2012 lived in more affluent areas as compared to recent

PV households and non-PV households. The decrease in the price of PV panels in recent years as

shown in figure D.5 has led to a boom in the residential solar market. However, this growth in

solar PV has not been uniformly distributed across the range of household incomes. Our analysis

of the Hawaiian solar market reveals that the diffusion trend is migrating to areas having lower

median income. This observation implies that there may be fewer barriers to solar adoption

18 Average home energy use per square foot is calculated by dividing each household’s average baseline pre-solar

electricity consumption by home size (sqft).

31

among lower income households than there were in the past, resulting in increased rates of

adoption in this consumer market segment.19

Homeownership

The percentage of owner-occupied housing units exhibits a similar trend to median income. In

figure D.9c, we observe that households that installed PV before 2012 were typically located in

areas with higher percentage of owner-occupied homes. Although the correlation between

owner-occupancy and PV adoption rates has lessened in recent years, it may still represent a

limit to the growth of PV adoption due to their requiring rooftops or outdoor/unshaded spaces.

In Oahu, roughly 42% of properties are renter-occupied and many owner-occupied properties are

located in multi-unit buildings or high-rises where it is technically unfeasible to install solar.20

This poses a particular challenge for solar diffusion growth given that renters do not have the

authority to install solar panels, reducing the number of potential solar PV installation sites.

Furthermore, even for properties where solar installations are technically feasible, rental property

owners are not incentivized to invest in PV since they generally do not bear financial

responsibility for electric bills. When tenants are responsible for paying for their own electricity,

landlords have no incentive to install PV systems. In arrangements where rent is fixed and

includes electricity cost, tenants have little to no incentive to conserve energy should the landlord

elect to install solar. As a result, landlords would bear the risk of paying for excess energy usage

on top of the cost of solar installation, discouraging them from adopting solar PV.

Education

Educational attainment is also an essential factor in determining the likelihood of PV adoption.

Figure D.9d demonstrates that the majority of PV adopters before 2012 resided in more educated

areas. Using educational attainment as a proxy for awareness of technology, highly educated

individuals are more likely to adopt solar as they are generally more knowledgeable and 19 In recent years, solar companies have offered a number of different financing options to prospective customers in

order to help offset the initial cost of solar installation. Potential PV adopters may elect to own their own systems by

buying them outright or borrowing against the value of their property through mortgage refinancing via tax

deductible “green energy” loan programs. For households with less financial liquidity and/or lower credit scores,

leasing options and Power Purchase Agreements are also available and require no large upfront expense. The variety

of financing options along with tax credits and other financial incentives will open the solar market to those with

limited access to capital, including lower income households and renters. 20 2011-2015 American Community Survey 5-Year Estimates

32

environmentally aware. Given the complexity of solar technology, it is not wholly unexpected

that early adopters were more highly educated. The declining trend in educational attainment

among PV households observed in figure D.9d may signify that the educational barrier to solar

technology has lessened as more readily understood information about the technology becomes

available through a variety of channels.

Family Size

We find that family size does not differ among PV and non-PV adopters. For each year of

installation, average household size is roughly identical to those without solar PV as seen in

figure D.9e.

2.5 Structural Model

The objective of this study is to explore the likelihood of households installing solar PV through

an evaluation of the determinants of solar PV adoption among residential households in Oahu,

Hawaiʻi. Towards this end, we develop a logistic regression model for PV technology adoption

wherein households make a decision in accordance with their preferences by maximizing the

utility of their energy consumption subject to limitations on their budget constraints. In

particular, we explore which factors drive household i to install a solar PV system. The model

dependent variable is a binary response, taking on the value of 1 if household i installs PV and 0

otherwise. That is,

Yi = 1 if a household i installs a PV system;

0 not install

The study employs several variables that are hypothesized to affect the likelihood of solar

adoption by residential single-family households. These relevant variables include households’

pre-solar electricity consumption, available solar resources, solar hot water heater (SWH)

installation, housing characteristics, and demographic information.

A household’s mean pre-solar consumption is calculated by averaging their monthly electricity

usage from 2000 to 2005, excluding any post-solar observations. This household average pre-

solar usage represents their baseline household energy demand before PV installation. To

measure available solar resources we use the maximum amount of solar resource available to a

33

given household during the 12-month pre-solar period. The presence of a SWH is captured via an

indicator variable that takes the value of 1 if a household has an installed SWH and 0 otherwise.

Household level characteristic variables include property value per square foot, age of the home

and home size. Demographic characteristics, which are gathered at the Census Block Group

level, include education attainment (percent of the population 25 years-old and over that have a

college degree or higher), average household size of occupied housing units, percentage of

owner-occupied homes, median age and median income.


Table C.2 reports the marginal effects of the logit model. We find that a household’s probability

of installing PV increases with their electricity consumption, confirming earlier findings in the

literature that higher energy consumption motivates installation of solar PV systems (Balcombe

et al., 2013). In California, Borenstein (2015) found that solar adoption was most prevalent

amongst the highest electricity users. This finding was due in large part to a steeply-tiered

electricity pricing structure under which sample households faced higher marginal prices at

higher-tiered usage levels. Although Hawaiʻi electricity rates are flat, high prices nonetheless

serve to incentivize households to reduce their electricity costs through solar adoption.

In addition to PV system size, PV energy output is largely determined by the availability of solar

resources at a household’s location. With greater solar resource availability, households can

expect higher energy production, leading to more substantial energy bill savings and a higher

return on investment. As a result, one would anticipate that consumers residing in areas having

greater available solar resources are more likely to invest in solar PV (Kwan 2012; Crago and

Chernyakhovskiy, 2014). However, the results of our study reveal that the amount of solar

resources available to Hawaiʻi households do not significantly impact their likelihood of solar

adoption. This deviation from the results of prior studies is largely due to the uniformity of solar

radiation levels across Oahu.

The results of this study are consistent with the findings of previous literature in consumers’

housing characteristics and demographic information (Keirstead 2007; Rothfield 2010; Leenheer

et al. 2011; Willis et al. 2011; Kwan 2012; Mills and Schleich 2012; Balcombe et al. 2013; Rai

and McAndrews 2012; Rai and Sigrin, 2013; Davidson et al. 2014; Langheim et al., 2014;

34

Chernyakhovskiy 2015; Graziano and Gillingham 2015). We find that housing characteristics,

reported in table C.2, statistically and significantly influence the probability of PV installation.

Empirical results indicate that the likelihood of solar adoption increases amongst individuals

residing in newer, larger and less expensive homes (measured on a per square foot basis). Newer

homes typically have better roof conditions which more easily facilitate PV system installation,

while larger homes are correlated with higher electricity consumption. Although the negative

relationship between home value and the likelihood of solar installation seems counterintuitive,

the result is nonetheless consistent with our descriptive finding shown in figure D.8b that most

PV homes have a lower cost per square foot than non-PV homes.

When considering demographic information, we find that the probability of solar adoption

increases in areas with higher median household income, smaller family size, lower median age,

and greater levels of educational attainment.21 Although previous studies have found that

motivation to adopt solar increases with family size (Keirstead 2007; Balcombe et al. 201), we

find a negative relationship between the probability of solar adoption and the number of

individuals in a household. Although larger households tend to consume more electricity, which

would lead to a higher probability of solar adoption, they are also more likely to be financially

constrained by other household expenses.

Homeownership is found to have an insignificant impact on solar installation despite our initially

predicting that homeownership would be highly predictive for solar adoption. This result may be

due in part to the influence of other attributes, such as age and income, which are highly

correlated with homeownership.

The presence of a SWH is found to have a significant effect on the likelihood of PV adoption,

with households having a SWH being inclined to invest in solar PV.22 This result is consistent

with our earlier finding, discussed in the Descriptive Evidence section, that PV homes are more

energy efficient.

21 The effects of these factors may not be straightforward due to interactions of a range of causal factors. 22 Note that in June 2008, Hawaii enacted legislation requiring SWH to be installed on all single-family new home

construction, with a few exceptions (S. 644, 2008). Due to this building energy code, the presence of SWH

installation may not be a significant indicator for the likelihood of solar adoption in the future. In the study sample,

we find that only 0.6% of PV homes with SWH were built after 2008.

35

2.7 Conclusion and Discussion

As national energy policy initiatives continue the push towards clean energy, exemplified in

Hawaiʻi’s embracing of 100% Renewable Portfolio Standards (RPS), there exists an increased

urgency to judiciously divest from traditional fossil fuel based technologies and re-tool using

renewable resources for distributed generations (DG) and other modern technologies.

Foundational planning models need to be enhanced through the integration of refined behavioral

knowledge in conjunction with physical grid constraints, so as to better support sustainable and

efficient diffusion of distributed PV.

To better support the integration of solar PV and other distributed energy resources, it is crucial

to understand the evolution and diffusion of solar PV technology. By evaluating the trends

underlying solar adoption on Oahu, this study revealed that the likelihood of solar adoption was

greatest in newer, larger, more energy efficient and less expensive (per square foot) homes.

Moreover, households living in areas with higher median household income, having smaller

family size, lower median age, and greater levels of educational attainment were found to be

more likely to install solar PV. We also found that having a SWH was the single strongest

predictor of solar PV adoption among residential single-family households.

Future research opportunities abound, including examining the growing trend in solar PV

adoption among non-residential customers. Beyond a per-kWh energy charge, such non-

residential customers are also subject to demand charges which determine the rate schedule to

which they belong.23 Due to this fundamental difference from residential households, their

motivations for PV adoptions can differ greatly from the factors reported on in this study. For

non-residential customers, PV installation can serve to drastically reduce their peak demand,

given their consumption is typically highest during daytime hours which corresponds with peak

solar PV energy production. As a result, the installation of solar PV lessens the probability of

their switching to higher pricing schedules, further reducing their cost of electricity.

Another topic worthy of further study is the potential of battery storage uptake. The rapid decline

in the cost of battery storage technology combined with changes to existing solar incentive

programs, which limit the amount of energy consumers can export to the grid, significantly

23 Demand charges are typically based on the highest level of electricity demand measured in kW.

36

increase the potential influence of battery storage in the near future. Additionally, since the

impact of battery storage discharge behavior on the electrical grid will likely differ significantly

from that of solar technologies, it is vital to assess how the grid may best leverage increased

distributed solar and battery storage penetration to help meet Hawaiʻi’s 100% RPS goal.

37

CHAPTER 3

Impact of Solar Adoption on Residential Electricity Demand

3.1 Introduction

Hawaiʻi has long struggled to identify practical and effective solutions to the unique challenges

facing its energy industry. These challenges arise in large part due to the state’s heavy reliance

on imported fossil fuels for energy generation and the isolated, self-contained, nature of its

electric grid. As a result, Hawaiʻi electricity prices are significantly higher than the U.S. national

average and, as shown in figure G.1, highly correlated with the price of crude oil.24

Given the high electricity prices in Hawaiʻi, the relative economic benefit derived from solar

photovoltaic (PV) technology is greatly enhanced, leading to a high rate of solar PV adoption.25

This study estimates electricity demand on Oahu, Hawaiʻi, examining not only how electricity

usage is impacted by price variations, but how the installation of solar PV and resulting solar PV

sizing decisions affect household electricity consumption patterns.

Figure G.2 illustrates the relationship between residential monthly electricity consumption in

kilowatt-hours (kWh) and electricity price for Hawaiian PV and non-PV customers in the study

sample from January 2000 to May 2016. It is observed that following the 2008 oil price shock,

which resulted in a spike in Hawaiʻi electricity rates, average energy demand has been steadily

declining. Clear seasonal patterns in average monthly consumption are observable within both

the PV and non-PV customer groups, although the trend begins to exhibit fluctuations towards

the end of the study period as solar PV penetration rises. Variations in consumption among PV

households between summer and winter months become more pronounced beginning in 2013

when the proportion of PV customers in the study sample exceeded 70%.

One of the most important questions relating to post-solar consumption behavior is whether PV

households consume more electricity following adoption. The intuition that solar PV adoption

results in increased electricity consumption stems from the perception that the marginal cost of

24 Over a 15-year period beginning in January 2000, the price of electricity in Hawaiʻi ranged from a low of 15

cents/kWh in 2003 to a high of 40 cents/kWh in 2008. 25 Cumulative PV installations have risen from under 1 megawatt (MW) installed capacity in 2005 to over 280 MW

in mid-2015, with over 95% being customer-sited installations.

38

electricity produced from solar systems is zero, thereby resulting in increased energy demand

amongst PV adopters. However, households that install rooftop PV systems are typically faced

with high upfront installation costs. The energy payback period and the manner in which the

installation is financed will dictate the true price of solar energy production for a given

household.

This study evaluates whether PV adopters exhibit changes in their energy demand, including

responsiveness to price and weather fluctuations, following installation of PV systems. An initial

examination of pre- and post-installation consumption trends within the sample dataset indicated

that PV households increase their electricity usage by approximately 3% in the first year

following PV adoption, with this growth rate gradually decreasing in ensuing years. Conversely,

non-PV customers exhibited consistently decreasing electricity consumption over the observed

time period. However, this cursory analysis considers PV adopters as a homogenous group.

To more clearly understand the impact of solar adoption on electricity consumption, this study

divides PV households on the basis of their PV sizing decisions. Towards this end, we first

define a set of three distinct PV sizing categories: Net Import, those who “under-sized” their PV

systems; Net Zero, those who sized their PV system to offset roughly 100% of their pre-solar

consumption; and Net Export, those who install “larger than necessary” PV systems. Using this

grouping, we find that the majority of households within the sample dataset fall under the Net

Zero group, with only 2% classified as Net Export households.

Following the division of PV households into distinct categories on the basis of their PV sizing

decisions, it is possible to assess how solar installation influences their electricity consumption

behavior. It was observed that Net Import households decrease consumption by approximately

4% in the first year following PV adoption. Conversely, Net Zero households consume more

energy after PV installation, increasing their electricity consumption by approximately 8% in the

first year following PV adoption. Net Export households exhibit the largest post-installation

increase in consumption, which increases by over 30% in the first year following installation and

by over 50% by the end of the fourth year post-installation.

In order to evaluate the dynamics of electricity demand in PV and non-PV households, an

empirical model was developed in this study. We first measure the “baseline” electricity demand

39

of PV and non-PV households utilizing pre-solar observations from January 2000 to December

2009. Analysis of this data reveals that electricity consumers are price-inelastic. In the baseline

period (2000-2009), the price elasticity of demand is similar for PV and non-PV households,

ranging from -0.14 to -0.10. When considering the previously defined PV sizing categories,

results reveal that in the baseline pre-solar period Net Export households exhibit the largest

response to changes in price, while Net Import households are the most inelastic. Non-PV and

Net Zero households are observed to have similar responsiveness to changes in electricity price.

We next estimate electricity demand utilizing both pre- and post-solar installation data spanning

the entire study period from January 2000 to May 2016. Household responsiveness to price and

weather variations is found to differ before and after installation of solar PV systems. Following

PV installation, household consumption becomes more sensitive to price variation, estimated

between -0.25 and -0.17. Clear differences are also observed between the various PV sizing

groups in both their pre-solar responses to price and the impact of installation on their price

response. Electricity consumption in Net Import and Net Zero households becomes more elastic

to price variations following PV installation. Conversely, Net Export households become less

responsive to price after installation of “over-sized” PV systems. This latter observation is not

entirely surprising when considering that Net Export households typically have an excess of

electricity at the end of each billing period. This natural excess in electricity produced versus

electricity demanded provides them sufficient overhead to alter their consumption without

concern for energy price fluctuations.

Results also demonstrate a statistically significant effect of weather on residential electricity

consumption. Temperature is found to have a strong positive correlation with energy

consumption levels. After solar installation, we find that PV households become more sensitive

to weather variations, especially to changes in temperature. This observation mirrors the earlier

descriptive evidence shown in figure G.2, suggesting increased variations in electricity

consumption between summer and winter months among PV households.

The remainder of the paper is organized as follows. Section 3.2 reviews literature related to this

study. Section 3.3 describes the proprietary dataset underlying the presented analysis and details

how each variable was processed. Section 3.4 and 3.5 introduce PV sizing categories and present

summary statistics and descriptive evidence for the data. Section 3.6 details the econometric

40

methodology used in the analysis, with estimation results reported in Section 3.7. Finally,

Section 3.8 offers concluding remarks and additional discussion of the results.


There is an extensive literature pertaining to demand for electricity that utilizes a wide variety of

econometric estimation methods including time series analysis, partial adjustment model (PAM),

generalized methods of moments (GMM), and ordinary least square estimation (OLS). Table F.1

presents a summary of the existing electricity demand studies in the literature. There is as yet no

clear consensus as to which methodology is most appropriate for electricity demand analysis.

These studies typically incorporate similar control variables, including income, weather,

demographic and dwelling characteristics, while employing different estimation procedures.

These variations can be attributed to the studies’ differing in their length of time covered by the

sample, demand sectors, types of data, and specification of prices. Despite these underlying

differences, the vast majority of studies find price elasticity of electricity demand to be inelastic.

A common challenge when evaluating the relationship between electricity consumption and

price variations is the endogeneity problem.26 Prior studies have generally assumed residential

households to be price takers since their electricity consumption behavior has little to no effect

on changes in electricity prices (Halvorsen and Larsen 1999; Shi et al. 2012). This study utilizes

disaggregated household-level data and a flat electricity price in Hawaiʻi. Therefore, we can

assume each residential household to be a price taker, thereby avoiding the endogeneity problem

in our electricity demand model.

Within this study, we employ a fixed effects model with the log-log functional form to assess

residential electricity demand. The fixed effects model controls for the impact of weather

variation through the inclusion of temperature, wind speed, and rainfall variables. The impact of

weather on electricity consumption has been widely studied in the literature (Kamerschen and

Porter 2004; Filippini 2011). In the residential sector, several studies have found that temperature

is a major determinant of household electricity demand (Silk and Joutz 1997; Hondroyiannis et

al. 2002). Other climatic variables including wind speed and humidity have been used as

26 Besides price endogeneity, another problem arises since PV installation is endogenous. Due to data limitation,

however, we are not able to find variables that can serve as valid instruments, leading to bias in the price elasticity

estimates.

41

correcting terms for the influence of temperature in energy consumption analyses (Engle et al.

1992; Li and Sailor 1995; Cancelo et al. 2008; Yan 1998).

In addition to the aforementioned electricity demand model, this study also explores whether

solar adoption leads to changes in electricity consumption behavior. A number of previous

studies have referred to such a change in electricity consumption behavior as the solar “rebound”

and “double-dividend” effects (McAllister 2012; Blackburn 2014; Deng and Newton 2016). The

notion of rebound effects has been extensively examined and reviewed in the energy efficiency

literature (Khazzoom 1980; Khazzoom 1987; Greening et al. 2000; Sorrell 2007: Sorrell et al.

2009). The rebound effect as outlined in these studies arises when energy consumption increases

as a result of improvements in energy efficiency. The direct rebound effect can be decomposed

into distinct income and substitution effects (Greening et al. 2000; Gillingham et al. 2015). The

income effect reflects the decrease in the cost of energy services leading to an increase in

households’ real income and increased consumption of alternative goods as a result of energy

efficiency improvements. The substitution effect captures the increase in energy consumption in

response to a change in relative prices. Conversely, the “double-dividend” effect leads to

increased conservation following adoption of energy efficiency measures.

Unlike other energy efficient appliances, PV systems are not energy consuming devices.

However, solar PV systems can considerably reduce electricity costs, theoretically incentivizing

households to consume more energy. There is as yet no clear consensus in the literature

regarding how the adoption of PV alters household consumption behavior. Employing

questionnaire data, Keirstead (2007) finds that there exists a solar “double-dividend” effect

among residential households following installation of PV systems. The author also finds that PV

adoption significantly improved awareness of both electricity consumption and generation.

However, this conclusion is drawn based on self-reported information and could, therefore, be

misleading.

Several studies have examined the role that pre-solar usage plays in predicting the effects of

solar adoption. Haas et al. (1999) find that solar adoption triggers increased levels of energy

conservation among high electricity consumers in Austria. High energy users in the

aforementioned study decreased their consumption after PV installation, while low energy users

showed a slight increase in energy demanded. Blackburn (2014) examined post-solar

42

consumption behavior and installation experience via survey and consumption data of residential

households in Texas, finding significant solar “rebound” and “double-dividend” effects arising

after PV installation.

In addition, McAllister (2012) leverages consumption and installation data of 5,243 Californian

households with solar PV to assess the impact of installing a solar system on electricity

consumption. The author examines patterns for system sizing and theorizes that grouping PV

customers on the basis of their pre-solar energy use would lead to a better understanding of post-

solar consumption behavior. The results of McAllister’s study show that the majority of PV

systems in the sample dataset were sized to offset approximately 20% to 80% of households’

total energy demand. Only 10% of the observed households were found to size their PV systems

to displace more than 100% of their pre-solar energy consumption. The author employs the

sizing categorization to evaluate the correlation between sizing decision and post-solar

consumption. The results indicated that PV households with “under-sized” systems relative to

their pre-solar usage tend to demonstrate decreased consumption following installation, whereas

those with larger systems were more likely to increase their level of consumption.

Although these prior studies revealed changes in consumption patterns pre- and post-solar

adoption, no comparison between PV and non-PV adopters was undertaken. Our study aims to

fill this gap in the literature by not only comparing energy usage patterns between pre- and post-

solar installation but also comparing consumption among PV and non-PV households.

3.3 Data Summary

3.3.1 Data Processing

In this study, we employ the same underlying data set from Hawaiian Electric Company (HECO)

utilized in Chapter 2 while incorporating additional electricity price and climatic variables.

Following Ito (2014), it is hypothesized that consumers respond to average price.27 Average

residential electricity price in this study was provided by the U.S. Energy Information

Administration (EIA) and Department of Business, Economic Development and Tourism

(DBEDT). To adjust the electricity price for inflation, the nominal electricity price was divided

27 Given the flat electricity pricing structure in Hawaii, marginal price is equal to the average price for consumers.

43

by the Consumer Price Index (CPI) for all urban consumers (all items) and then multiplied by the

annual average of 2015.28 This adjustment has the effect of normalizing all electricity prices to

2015 dollar values. To account for the effect of weather variation on electricity consumption, the

monthly maximum temperature (Fahrenheit), average wind speed (miles per hour) and total

precipitation (inches) were obtained from the National Weather Service (NWS) for Honolulu

International Airport weather station.

We also determine, for each PV household, whether additional PV systems have been added to

their accounts during the observed time period. It is crucial to validate whether PV customers

have additional installed systems in order to accurately calculate their gross electricity

consumption and determine their appropriate sizing category. Additional information detailing

the number of add-on systems, their size, and the date of installation for each additional system

was added using HECO’s internal data portal. From this process, 397 PV accounts were

identified which had installed at least one additional PV system after the initial PV installation.

Such accounts were excluded from our analysis, leaving 2,093 PV and 1,557 non-PV households

remaining in the sample data set.29

Next, monthly solar electricity produced by rooftop PV is estimated. Let Iit be the solar

irradiance measured at a household i at time t (Watt/m2) and Si be a PV system size of a

household i. The estimated monthly solar electricity produced by a rooftop PV for a household i

at time t (Eit) is calculated as:

Eit = Iit* Si (3.1)

To accurately estimate PV energy output over the course of a solar system’s lifespan, we apply a

0.06% degradation rate per month to the estimated PV energy production (Jordan and Kurtz

2013). Let α be the number of months after the month of PV installation, then the degraded PV

energy output of a household i at time t (DEit) is calculated as:

DEit = Eit*(1.0006)-α (3.2)

28 Source: Consumer Price Index for All Urban Consumers: All items in Honolulu, HI (MSA), Federal Reserve

Bank of St.Louis. 29 PV households with additional PV systems installed were excluded from this study to assure that none of the PV

households have transitioned from one PV sizing group to another during the study period.

44

In order to calculate gross electricity consumption, it is necessary to identify the month in which

the new PV panels become operational. The installation date referenced in the dataset refers to

the date of approval of the interconnection agreement submitted by the customer and does not

always represent the actual date of installation. To mitigate this issue, we identify the first

subsequent month in which a significant reduction in net monthly consumption is detected.

These observations are then used to revise the installation date of each PV customer accordingly.

Gross electricity consumption is calculated by adding the degraded monthly PV energy output

(DEit) to net electricity consumption:

GkWhit = NkWhit + DEit (3.3)

where GkWhit and NkWhit are gross and net electricity consumption of a household i at time t,

respectively. Although we previously adjusted the actual installation date to better reflect the

time of installation, three additional observations – one month before, one month after and the

estimated actual month of installation – are excluded for each customer to ensure clean pre- and

post-solar consumption measurements.

3.3.2 Summary Statistics

Two distinct study datasets, baseline and overall, are considered in the analysis. The baseline

dataset spans the period from January 2000 to December 2009 and excludes observations

occurring after PV installation for each household. The overall dataset consists of all

observations, both pre- and post-solar, from January 2000 to May 2016. Analysis of the baseline

dataset is used to illustrate the starting point of households in each customer group, whereas

analysis of the overall dataset enables us to assess the impact of PV adoption on household

electricity consumption.

Table F.2 shows summary statistics of monthly electricity consumption. Comparing consumption

of non-PV and PV households during the pre-solar period (2000-2009), it is observed from table

F.2 that households who are more likely to install PV consume more electricity than those who

are less likely to install PV. When comparing pre- and post-solar installation over the whole

study period (January 2000 – May 2016), residential single-family households with PV use less

electricity on average after PV installations.

45

Net usage represents the difference in electricity bought and sold by a household. At the

conclusion of each billing period, households pay the utility for their net electricity usage. A

negative net usage value represents the amount of energy credit a PV household receives from

the utility. Households with negative net energy usage only pay the minimum surcharge. It is

observed in table F.2 that for PV households, post-solar net electricity consumption is

substantially lower than gross electricity usage, with a minimum of -2,240 kWh.

Table F.3 shows summary statistics for the set of control variables including electricity price,

solar PV system size in kilowatt (kW), and various climatic variables. In the next section, the

subcategorization of PV households on the basis of their PV sizing decisions and associated

descriptive evidence is presented.

3.4 PV Sizing Decisions

Potential PV customers are faced with a number of necessary steps when first adopting solar. In

order to identify the PV system size that best fits their needs, a household must first analyze their

present electricity consumption along with any future projected increases or decreases in

electricity demand. For example, a household may be planning to purchase an electric vehicle

(EV) and install a home EV charger, leading to increased electricity usage. If the aforementioned

household’s goal is to cover 100% of their electricity requirements using solar energy then an

“over-sized” PV system may be desirable when taking into account their anticipated

consumption increase. In contrast, if a household anticipates reduced electricity demand in the

future then a smaller PV system may be more appropriate to meet their needs.

Prospective PV adopters must also choose a PV energy production goal to offset their electricity

usage. While some homeowners elect to install PV systems that offset 100% of their grid

electricity demand, others opt for smaller systems with lower energy offset percentage in order to

reduce the cost of solar installation and accelerate return on investment. Policies and associated

regulations may also serve to influence households’ solar sizing decisions. In California, for

example, utilities do not compensate systems larger than the electricity used by a household in

the previous year. Therefore, households are typically limited to PV system sizes that offset no

more than their annual onsite electricity load. McAllister (2012) found that the solar energy

generated by PV adopters canceled out the higher-tiered-rate charges each month, leaving PV

46

adopters with only the baseline rate to pay. These PV households are therefore better off

financially with the lower percentage energy offset.

In Hawaiʻi, no such regulations have been implemented, although there is a system capacity limit

of 100 kW for Net Energy Metering (NEM) program customers. NEM customers are allowed to

return all of their excess energy produced by PV systems to the grid, receiving full retail rate

credit to their account. In addition, these energy credits may be carried over to the next month if

unused. At the conclusion of each 12-month reconciliation period, any unused credits remaining

in a NEM customer’s account are zeroed out and the process begins again. These generous

compensation policies incentivize PV customers in Hawaiʻi to install larger-than-necessary solar

systems.

In the ensuing section, we analyze customers’ solar sizing decisions to determine whether the

“over-sizing” PV installation trend actually exists in Hawaiʻi. The rational choice for a

prospective PV household is to choose a PV system size that not only minimizes their payback

period, but also maximizes the utility of any planned future energy consumption. “Optimal”

system size can, therefore, vary greatly between different households depending on their 12-

month pre-solar electricity consumption and anticipated future needs. “Optimal” PV system size

is also dependent on a variety of other factors such as shading obstruction, roof condition,

available rooftop space for PV module placements, the orientation and tilt of the system, solar

resource availability, and financial considerations.30 High temperatures also negatively affect

solar panel efficiency, and can significantly lessen PV energy production (Skoplaki and Palyvos

2009). This decrease in efficiency is due to the fact that as the temperature of a PV panel rises;

its output current increases exponentially, linearly reducing voltage output.

After taking all of these factors into account, we define the “optimal” solar system size as the one

designed to offset, at most, 100% of a household’s average 12-month pre-solar electricity usage.

Given a customer’s preceding 12-month of electric bills prior to solar installation, and the

available sunlight at the proposed array site, we apply a rule of thumb for calculating the

“optimal” PV system size for a given household i (OSi) as follows:

30 Households’ decision to size rooftop PV may also be impacted by outside factors. For example, solar contractors

and installers may influence a household’s PV sizing decisions by suggesting a larger or smaller system than is

financially optimal.

47

OSi = Prei (3.4)

CF*24*31

where Prei is an average of monthly kWh that household i consumed during the 12 months prior

to PV installation. Solar Capacity Factor (CF) is the ratio of actual power generation over a

given time period and the installed (nameplate) capacity of the solar PV system.

Examining 2013 and 2014 data, monthly CF for Oahu ranges from 13.2% to 22.7%, with an

average of 18.4%.31 Instead of using the average value of CF, the maximum and minimum CF

values are employed to calculate the “optimal” size band. The lower (OSi) and upper (OSi)

bounds of the band of a household i are calculated as follows:

OSi = Prei (3.5)

0.227*24*31

OSi = Prei (3.6)

0.132*24*31

The lower and upper bounds represent the effect of seasonal variations in weather, solar

resource, and household electricity demand. The “optimal” size band varies amongst households

depending on their 12-month pre-solar average usage. PV households are categorized on the

basis of where they are located relative to the “optimal” size band. PV households are

categorized as Net Zero if their PV system size falls within the band. Those with rooftop PV

system larger than the upper bound of the band are categorized as Net Export, while those with

PV systems smaller than the lower bound are categorized as Net Import. From a sample of 2,093

residential single-family households with solar PV, we find that approximately 2% of households

are categorized as Net Export, 41% as Net Import, and the remaining 57% as Net Zero.

Household percentage energy consumption offset is calculated based on 12-month average pre-

solar electricity consumption and PV energy output. Figure G.3 shows that on average PV

households belonging to the Net Import group sized their rooftop PV systems to displace

approximately 59%, PV households belonging to the Net Zero group sized their rooftop PV

systems to displace approximately 106%, and PV households belonging to the Net Export group

31 Source: HECO

48

sized their rooftop PV systems to displace approximately 163% of their electricity consumption

by their PV systems. The installation trend for households within each sizing group is shown in

figure G.4. It is observed that the majority of earlier adopters were classified as Net Import

households, with a small number of Net Zero households.

The relationship between households’ pre-solar electricity consumption and their choice of solar

PV system is further examined in figure G.5. It compares 12-month pre-solar monthly usage of

PV households across the aforementioned sizing groups, illustrating that Net Import households

consume more electricity, while Net Export households consume less. Figure G.6 examines the

distribution of solar system size for the different PV sizing categories. We find that Net Import

households installed smaller PV systems relative to the other groups, with Net Zero and Net

Export households having similar PV system size distribution. These two figures reveal that PV

households who “over-sized” their solar systems did not necessarily install significantly larger

systems than households in the other groups, but rather consume less electricity relative to the

size of their PV system.

Table F.4 reports summary statistics of households’ electricity consumption in each customer

group using both the baseline and overall datasets. In the overall dataset, the average net monthly

usage of Net Export households is observed to be negative. This indicates that the amount of

energy returned to the grid by these households exceeds that which they purchase from the

utility, resulting in minimum electric bills following PV installation.

3.5 Consumption Trend

Figure G.7 depicts average annual electricity usage and percent year-over-year change,

delineating differences in energy consumption patterns amongst PV and non-PV households

within each sizing group. It is observed that there exists a slight difference in consumption levels

between the different customer groups, with Net Export households being the lowest energy

users and Net Import households the highest.

In observing the percent year-over-year change in figure G.7, we see that Net Export households

exhibit a larger decline in energy demand in the period between 2004 and 2011. However, after

2011 their usage significantly increases as the percentage of customers with PV within the sizing

49

group increases. The largest decline in consumption for Net Import households is observed in

2012, corresponding with the sharp rise in electricity prices in 2011

The next section will further investigate whether there is an observable “rebound” or “double-

dividend” associated with PV installations by analyzing changes in energy consumption behavior

of PV households before and after PV adoption.

3.5.1 Comparisons: Pre-Solar VS Post-Solar Consumption Behavior

In order to analyze household consumption behavior before and after PV installation, a solar

time trend, measuring solar gross electricity consumption in the two years pre-solar and four

years post-solar, is constructed. Figures G.8 and G.9 illustrate average trends in electricity

consumption for PV and non-PV households. We observe that non-PV households lower their

electricity use, but at a gradually decreasing rate. This decreasing trend in electricity

consumption may result from a change in energy use behavior in response to price and/or

weather variations and/or home energy efficiency improvements.32 Given the limited information

on energy efficiency efforts made by households in our dataset, we are unable to parse their

impact on household electricity consumption. However, it is probable that the declining trend in

energy use among non-PV households is due largely in part to increased energy efficiency

saturation.

Figure G.9 shows that, on average, PV households increase their energy consumption after PV

installation. Comparing electricity consumption pre- and post-installation, we observe a 3%

increase in the first year following PV installation. The rate at which electricity consumption

increases for these households falls in ensuing years after this initial jump. This observation

implies that although PV customers adjust their electricity consumption behavior in the period

immediately after PV adoption, the overall impact of this rise is muted by the subsequent decline

in the years following.

Figures G.8 and G.9 also show significant differences in post-solar consumption trends among

households belonging to each PV sizing category. When compared to their 12-month pre-solar

usage, Net Import households consume 4% less electricity in the first year post-installation. Net

32 In June 2009, Hawaiʻi established its Energy Efficiency Portfolio Standard (EEPS) setting a goal of electricity

reduction by 4,300 gigawatt-hours (GWh) by 2030. Hawaiʻi EEPS has successfully accelerated energy efficiency

resources deployment. Source: www.dsireusa.org

50

Import households have an average percent energy offset of 59%, meaning that even after solar

installation they are still left with positive electric bills. Therefore, after solar installation, these

households may elect to modify their consumption behavior and/or adopt other home energy

efficiency improvements to further conserve energy. Doing so enables their solar system output

to cover a higher percentage of their overall demand, thereby reducing the cost of electricity and

accelerating the return on investment of their PV installation.

Net Zero households increase their energy usage by approximately 8% after PV installation.

However, this consumption trend declines in subsequent years, indicating a slight adjustment to

their electricity consumption behavior follow PV installation.

In contrast to the other two PV sizing groups, Net Export households demonstrate a clear

increasing trend in post-solar energy usage. The post-solar consumption of Net Export

households increases by over 30% on average in the first year following PV installation, and

further increases each year thereafter. It is not altogether surprising that Net Export households

with “over-sized” PV systems increase their energy use following installation. Some of these

households may have planned to increase their energy usage due to an anticipated change in their

needs, such as the purchase of an EV. Moreover, the excess energy produced by “over-sized” PV

systems may be perceived as “free”. Having a substantial electricity surplus and paying only the

minimum surcharge on their monthly electric bills, Net Export households have considerable

incentive to increase their consumption after PV adoption.

Our descriptive evidence further reinforces earlier findings by McAllister (2012) that households

with “under-sized” PV systems tend to decrease their energy consumption, while those with

“over-sized” PV systems tend to increase their energy consumption after PV installation. As in

these previous studies, we have observed that solar “rebound” and “double-dividend” effects

among PV adopters are highly correlated with their sizing decisions.

3.6 Statistical Model

The ensuing section evaluates the relationship between residential electricity demand and its

relevant influencing factors for 3,650 households – 1,557 non-PV and 2,093 PV adopters – on

Oahu, Hawaiʻi. We hypothesize that residential electricity demand is dependent on the price of

electricity, weather variation and seasonal patterns, the business cycle, household demographic

51

and socioeconomic characteristics, and PV installation. The general electricity demand model

can be represented by the following function:

Yit = f(Pt-1, Weathert, Seasonal Trendt, Business Cyclet, PVit, Xi) (3.7)

where Yit is household i’s electricity consumption in kWh at month t. The variable PVit indicates

the time t at which household i installed PV. Pt-1 is average residential electricity price in cents

per kWh at time t-1. Given that households typically receive price information in their electric

bills at month’s end, we hypothesize that the previous month’s electricity price dictates their

electricity consumption decisions in the subsequent month. The effect of weather variation is

controlled by including maximum temperature, average wind speed and total precipitation in the

regression model. Household characteristics and demographics (Xi) are accounted for using

household fixed effects. The impact of seasonality and the business cycle on residential

electricity usage is captured via month and year fixed effects.

Based on equation (3.7), we employ a log-log functional form to model residential electricity

demand. We first estimate the “baseline” energy consumption of PV and non-PV households

from January 2000 to December 2009, excluding post-installation observations. Formally, we

posit the following empirical baseline (pre-solar) model:

ln(Yit) = β0 + β1 ln(Pt-1) + β2 ln(Pt-1) PVi

+ β3 ln(Tempt) + β4 ln(Windt) + β5 ln(Raint)

+ β6 ln(Tempt) PVi + β7 ln(Windt) PVi + β8 ln(Raint) PVi

+ γi + um + vy + εit (3.8)

The baseline model in equation (3.8) captures underlying differences in consumption of

residential PV and non-PV customers in the period before PV installation, along with the impact

of weather fluctuations on their respective energy usage. The PV dummy variable, PVi, is set

equal to 1 if household i is observed to have installed a PV system at any time during the study

period, and equal to 0 if it did not. Three climatic variables are included in the electricity demand

model: (1) maximum temperature measured in degrees Fahrenheit (Tempt); (2) average wind

52

speed in miles per hour (Windt); and (3) total precipitation in inches (Raint). Relevant household

characteristics are controlled for using household fixed effects (γi). Month and year dummy

variables, um and vy, capture the impact of seasonal factors and the business cycle on electricity

consumption.

To determine the impact of solar adoption on consumption we utilize a post-solar dummy

variable (τi), which is set equal to 1 for periods following solar adoption and 0 otherwise, for a

given household i. We theorize that PV adoption not only influences the manner in which

residential households alter their consumption in response to changes in price, but also their

sensitivity to weather variations. Data for the entire study period (January 2000 – May 2016),

including both pre- and post-solar observations, is used to estimate our overall (pre- and post-

solar) demand model which can be expressed as:

ln(Yit) = β0 + β1 ln(Pt-1) + β2 ln(Pt-1) PVi + β3 ln(Pt-1) PVi 1(t>τi)


+ β7 ln(Tempt) PVi + β8 ln(Windt) PVi + β9 ln(Raint) PVi

+ β10 ln(Tempt) PVi 1(t>τi) + β11 ln(Windt) PVi 1(t>τi) + β12 ln(Raint) PVi 1(t>τi)

+ γi + um + vy + εit (3.9)

The sizing of solar PV systems is captured by replacing the PV dummy variable (PVi) in

equation (3.8) and (3.9) with sizing group dummy variables. Let NIi, NZi, NEi equal 1 for

household i if it belongs to the Net Import, Net Zero or Net Export sizing groups, respectively,

and 0 otherwise. Upon replacing the PV dummy variable in this manner, our model of baseline

consumption by sizing group is:

ln(Yit) = β0 + β1 ln(Pt-1) + β2 ln(Pt-1) NIi + β3 ln(Pt-1) NZi + β4 ln(Pt-1) NEi


+ β8 ln(Tempt)NIi + β9 ln(Windt) NIi + β10 ln(Raint) NIi

53

+ β11 ln(Tempt)NZi + β12 ln(Windt) NZi + β13 ln(Raint) NZi

+ β14 ln(Tempt)NEi + β15 ln(Windt) NEi + β16 ln(Raint) NEi

+ γi + um + vy + εit (3.10)

and the resulting overall consumption by sizing group model is:

ln(Yit) = β0 + β1 ln(Pt-1) + β2 ln(Pt-1) NIi + β3 ln(Pt-1) NZi + β4 ln(Pt-1) NEi

+ β5 ln(Pt-1)NIi 1(t>τi) + β6 ln(Pt-1) NZi 1(t>τi) + β7 ln(Pt-1) NEi 1(t>τi)


+ β11 ln(Tempt)NIi + β12 ln(Windt) NIi + β13 ln(Raint) NIi

+ β14 ln(Tempt)NZi + β15 ln(Windt) NZi + β16 ln(Raint) NZi

+ β17 ln(Tempt)NEi + β18 ln(Windt) NEi + β19 ln(Raint) NEi

+ β20 ln(Tempt) NIi 1(t>τi) + β21 ln(Windt) NIi 1(t>τi) + β22 ln(Raint) NIi 1(t>τi)

+ β23 ln(Tempt) NZi 1(t>τi) + β24 ln(Windt) NZi 1(t>τi) + β25 ln(Raint) NZi 1(t>τi)

+ β26 ln(Tempt) NEi 1(t>τi) + β27 ln(Windt) NEi 1(t>τi) + β28 ln(Raint) NEi 1(t>τi)

+ γi + um + vy + εit (3.11)


3.7.1 No-PV & PV

Baseline Model – Pre-Solar Period (January 2000 – December 2009)

We first estimate electricity demand of residential households with and without PV. Empirical

results in specification (1) of table F.5 demonstrate that both PV and non-PV households are

price-inelastic in the pre-solar period. Their respective price elasticities of electricity demand are

54

both found to fall between -0.12 and -0.10. This implies that, ceteris paribus, a 10% increase in

price is estimated to result in approximately a 1% to 1.2% decrease in total energy consumption

It is also found that wind speed and precipitation have a statistically significant, albeit small

impact on household electricity consumption. As anticipated, the coefficient of temperature is

positive and statistically significant, indicating that households consumed more electricity as

temperature increased during the pre-solar period. PV households were found to be more

responsive to temperature variations than were non-PV households.

Overall Model – Pre & Post-Solar Period (January 2000 – May 2016)

We next examine the effects of PV installation over the whole study period including both pre-

and post-installation observations. Results detailed in specifications (2) and (3) of table F.5

reveal that PV households become slightly more sensitive to variations in price and weather after

solar installation, with the post-solar price elasticities of PV households estimated between -0.25

and -0.17. Specification (3) of table F.5 reflects additional controls for the impact of weather on

post-solar electricity consumption. Empirical results under this analysis indicate that the effect of

an increase in temperature differs significantly for households before and after PV installation.

For PV households, a 10% increase in temperature results in a 0.6% increase in electricity

consumption before solar adoption, and a 13.8% increase in electricity consumption following

solar adoption.

3.7.2 No PV & PV by Sizing Group

Baseline Model – Pre-Solar Period (January 2000 – December 2009)

Initial sizing decisions are also shown to be a predictive factor of electricity consumption for PV

households. Regression results presented in table F.6 indicate that non-PV and Net Zero

households demonstrate similar price elasticities in the pre-solar period, while households that

install “over-sized” PV systems are the most price-elastic. These results suggest that prior to PV

installation; Net Export households are more sensitive to price variations relative to those

households belonging to other sizing categories. The choice to install “over-sized” PV systems,

capable of producing more electricity than they typically require, therefore provides them with a

buffer against unexpected price fluctuations.

55

Net Import households, although found to be the most responsive to weather variations, are

observed to be the least responsive to price. Intuitively, these households may have been more

disciplined than others in regards to their electricity usage, meaning that changes to electricity

price have minimal impact on their consumption. Due to this dynamic, there was little need for

them to “over-size” their PV systems to offset electricity demand levels exceeding their normal

use-state.

Overall Model – Pre & Post-Solar Period (January 2000 – May 2016)

Specifications (5) and (6) of table F.6 demonstrate that Net Import and Net Zero households

become more responsive to changes in price after solar adoption. The price elasticities of

demand for Net Import households are found to change from -0.01 to -0.18 post-solar, while the

price elasticities of demand for Net Zero households are found to change from -0.09 to -0.22,

during the pre- and post-solar periods, respectively. These changes in price sensitivities suggest

that PV adoption leads to increased awareness of electricity demand amongst Net Import and Net

Zero households.

Empirical results reveal that although the estimated price elasticity of Net Export households

who “over-sized” their PV systems become less negative, it is not a statistically significant

change. This result is not altogether surprising, as the PV installations of these households are

sized to offset considerably more energy than they typically require. Unlike PV households in

other sizing categories, Net Export households are able to consume more electricity without

increasing their monthly electric bill beyond the minimum monthly surcharge.

Results to this point have demonstrated that PV adoption triggers a significant improvement in

energy use awareness, leading to a corresponding change in consumption behavior. Due to the

high cost of solar installations, many households attempt to maximize their return on investment

by modifying their consumption behavior. Moreover, these same households are more attentive

to other factors relating to their post-solar consumption including electricity price, the

performance of their PV systems, the amount of energy credits carried over from the previous

month, and variations in weather and solar resources. Prior studies on the impact of PV

installation have also noted an increase in electricity use awareness amongst PV adopters

(Keirstead 2007; Rai and McAndrews 2012). Although data availability limits our ability to fully

explain the underlying motivators of this increase in awareness, we have nonetheless shown

56

marked changes in consumption behavior before and after solar installation within both the

presented descriptive evidence and empirical analysis.

3.7.3 Additional Findings

Our results have indicated that the majority of households in the study sample chose to size their

PV systems to offset roughly 100% of their pre-solar average electricity consumption. However,

these findings were based on observations of customers provided with adoption incentives

through the NEM program. In October 2015, the Hawaiʻi Public Utilities Commission issued a

ruling ending NEM for all new customers. At present, the Hawaiian Electric Company offers

customers two new types of tariffs, consumer self-supply (CSS) and consumer grid-supply

(CGS). The CSS tariff does not enable PV customers to send excess energy generated back to the

grid and any exported energy is not compensated by the utility. The CGS tariff more closely

resembles the now defunct NEM program, excepting that CGS pays customers a reduced price

for excess energy exported to the grid. These policy changes increase the opportunities for new

technologies and business models leveraging battery storage and demand flexibility, which

provide customers with greater flexibility and enable them to better respond to changing grid

conditions.

Under the newly introduced CSS and CGS tariffs, PV customers are no longer as incentivized to

“over-size” their rooftop PV systems as they were under NEM. Due to the drastically decreasing

value of exported energy, “over-sizing” PV systems results in a higher initial PV installation cost

without the corresponding return on investment provided under NEM. This change in individual

household incentives may, however, result in increased overall social welfare since the

combination of households with “over-sized” systems and PV penetration limits imposed by the

utility have deprived many new households of the opportunity to install rooftop solar.

According to the Kauaʻi Island Utility Cooperative and the Hawaiian Electric Companies, the

typical household consumes approximately 25% of its electricity between 9 a.m. and 3 p.m. The

previously discussed PV sizing calculation can be modified based on daytime pre-solar energy

usage of households in our sample. We assume that a “daytime right-sized” PV system is one

57

designed to offset roughly 25% of a household’s average pre-solar consumption.33 Following this

adjustment, 95% of households in the study sample are categorized as Net Export and fewer than

2% of households are categorized as Net Import. This result implies that the majority of NEM

customers export excess PV energy to the grid during daytime hours.

Based on our “all-day right-sized” PV sizing category discussed in section 3.4, figure G.10

displays the proportion of exported energy relative to overall estimated PV energy output. The

average PV household exports approximately 59% of their PV energy output to the grid, with

Net Export households being the highest at 67% on average.34 Monthly energy costs for NEM

households reflect the difference between the amount of electricity that they purchase from the

utility, and the amount that they sell back to the grid. Figure G.11 illustrates the distribution of

net monthly energy usage of PV households broken down by PV sizing group. It is observed that

Net Export households typically exhibit negative net usage, under which they are only

responsible for paying the monthly minimum surcharge, with any excess energy credits carrying

over to the next month.

These results suggest that there is no economic benefit for customers to “over-size” their solar

PV and over-produce electricity under CGS due to the limited compensation received for excess

energy produced and the inability to carry credits over to the next month. Due to this, it is crucial

for CGS customers to “right-size” their PV systems in order to maximize their return on

investment.

3.8 Conclusion and Discussion

To better understand the true impact of solar PV adoption on electricity consumption, a rigorous

analysis using disaggregated data is required. This study first examined how PV and non-PV

customers alter their energy usage over time. Findings indicated that PV adoption has a

significant impact on household electricity consumption, with the majority of PV households

found to increase their electricity consumption following installation while at the same time non-

PV households were decreasing their electricity demand.

33 The calculation for PV sizing is the same as that mentioned in section 3.4, but each household’s average pre-solar

consumption is reduced to 25%. 34 Net Zero and Net Import households export approximately 55% and 64% of their PV energy output to the electric

grid, respectively.

58

PV households were categorized on the basis of their PV sizing decisions, enabling a more

granular examination of their pre- and post-solar consumption trends. This analysis revealed the

presence of both solar “rebound” and “double-dividend” effects in the study sample. Households

with “under-sized” PV systems were found to consume less, whereas those with “right-sized” or

“over-sized” were found to consume more electricity following solar installation.

Changes to household electricity consumption in response to price and weather variations were

also examined. An empirical study of consumption data revealed that customers became more

sensitive to such variations post installation. Households with “over-sized” PV systems were

more price-inelastic, while households belonging to the other two sizing groups were more price-

elastic following solar installation. Temperature was found to have a stronger positive impact on

residential electricity demand following PV installations, leading to increased variation in

consumption between summer and winter months.

Although the NEM program was ended in the last quarter of 2015, the majority of current PV

customers in Hawaiʻi are grandfathered under the NEM tariff conditions. It is therefore essential

to understand behavioral patterns of NEM customers in spite of the program ending. Our

findings provide valuable insights, from both utility and policy perspectives, into how changes in

price may alter household electricity usage following PV adoption. As electricity consumption

behavior encompasses both the overall quantity of electricity used and the time of day at which it

was consumed, analyses leveraging time-of-day consumption data will shed light on possible

load shifting and the potential benefits of battery storage technologies.

Results clearly demonstrated that “over-sizing” PV discourages energy conservation in

households. The shift from NEM to CSS and CGS tariffs can be therefore viewed as an

important policy shift, with the newly enacted tariffs designed to encourage “right-sizing”

amongst new PV customers. However, CSS and CGS customers are unlikely to behave similarly

to NEM customers, making continued study of customers’ consumption behavior under these

new pricing structures vital to the design of effective policies and incentive programs.

59

Appendix A

Tables for Chapter 1

Table A.1: Summary Statistics of Variables at Distribution Transformer Level.

Variables Mean SD Min Max

Variations (SD) in Net Electricity Load (kW)a 270.9 213.4 3.1 1,800.5

Daytime (Net) Minimum Load (kVA) 2,230.4 896.1 108 4,412.2

Customer Mix Total Number of Customers 1,790.9 1,150.2 45 5,459

Number of Residential Customers 1,606.0 1,125.1 0 5,256

Number of Commercial Customers 184.9 124.4 7 520

Percentage of Residential Customers (%)b 79% 29% 0 99%

Weather Average Temperature (Celsius) 24.4 3.1 16.8 31.6

Average Humidity (%) 71% 9% 48% 88%

Average Wind Speed (mph) 7.8 2.6 3.00 13

Average Solar Irradiance (unitized 0-1) 0.2 0.3 0 0.9

Solar Capacity PV Installed Capacity (kW)c 631.9 658.4 0 4,756.4

a Net load is defined as the amount of electricity met by utility generation, covering a period from September 2010

to May 2014b Percentage of residential customers is calculated by dividing the number of residential customers by total number

of customers on each transformer.c PV installed capacity represents cumulative solar (nameplate) capacity of executed agreements on Net Energy

Metering, feed-in-tariff and standard interconnection agreement programs.

Source: HECO

60

Table A.2: Volatility of Net Electricity Load by Time, Seasons, and Year.

Standard Deviation of Net Load (kW) Mean SD Min Max

Time of Daya Day 385.9 249.4 3.6 1,800.5

Night 210.6 162.0 3.1 1,789.0

Seasonb Summer 261.8 215.5 3.1 1,746.9

Winter 278.2 211.4 4.5 1,800.5

Year 2010 237.6 156.4 9.8 1,089.7

2011 255.6 197.9 3.1 1,680.7

2012 260.7 214.9 4.3 1,800.5

2013 280.7 220.2 3.6 1,789.0

2014 300.7 218.4 4.5 1,593.8

a Daytime is defined from 9:00am to 5:00pm whereas nighttime is from 5:15pm to 8:45am.

b Summer months are from May to October and winter months are from November to April.

61

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log

of

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(0.0

28)

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29)

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29)

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29)

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pera

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0.0

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76***

0.0

78***

0.0

77***

0.0

79***

(0.0

24)

(0.0

24)

(0.0

24)

(0.0

24)

Tem

pera

ture

*H

um

idit

y-0

.039

***

-0.0

39

***

-0.0

41

***

-0.0

41

***

(0.0

11)

(0.0

11)

(0.0

11)

(0.0

12)

Co

nst

ant

5.1

60***

5.1

84***

5.2

61***

4.5

24***

5.2

87***

4.5

48***

4.6

09***

4.6

36***

(0.2

33)

(0.2

33)

(0.2

27)

(0.2

99)

(0.2

27)

(0.3

01)

(0.3

02)

(0.3

05)

No

te:

Day

time

is fro

m 9

:am

to

5:0

0pm

. N

umer

of o

bse

rvat

ions

is 1

15,8

26.

Sta

ndar

d e

rro

rs a

re in

par

enth

eses

and

clu

ster

ed a

t tr

ansf

orm

er le

vel.

*,*

*,

and

***

ind

eica

te

signif

icance a

t th

e 9

0%

, 95%

, and 9

9%

level,

resp

ectively

.

Dependent

Va

ria

ble

: L

og

of

SD

of

Net

Lo

ad

Tab

le A

.4:

Em

pir

ical

Res

ult

s – D

ayt

ime

On

ly.

63

Appendix B

Figures for Chapter 1

Figure B.1: Annual Solar Installed Capacity by Customer Segment.

64

Figure B.2: Variations in Net Electricity Load – Residential.

Figure B.3: Variations in Net Electricity Load – Commercial.

Figure B.4: Variations in Net Electricity Load – Industrial.

Source: HECO.

Source: HECO.

Source: HECO.

An

nu

al

Av

era

ge

Net

Ele

ctri

city

Lo

ad

(k

W)

PV

In

sta

lled

Ca

pa

city

(k

W)

PV

In

sta

lled

Ca

pa

city

(k

W)

PV

In

sta

lled

Ca

pa

city

(k

W)

2011 2012 2013 2014

2011 2012 2013 2014

2011 2012 2013 2014

An

nu

al

Av

era

ge

Net

Ele

ctri

city

Lo

ad

(k

W)

An

nu

al

Av

era

ge

Net

Ele

ctri

city

Lo

ad

(k

W)

65

Figure B.5: 7-Day Net Load Profiles – Residential, Commercial, Industrial Areas.

Note: Data used in this figure covers a one-week period from 8/28/2011 to 9/3/2011.

Source: HECO.

66

Figure B.6: Relationship between Temperature and Humidity – Sun & No Sun.

Figure B.7: Average Solar Irradiance by Time-of-Day – Winter & Summer.

Source: HECO.

Source: HECO.

67

Figure B.8: Volatility of Net Electricity Load.

Source: HECO.

Note: Standard deviation of net electricity load in each 15-minute interval is used to

represent variations in net electricity load. Outliers are excluded.

68

Fig

ure

B.9

: N

et E

lect

rici

ty L

oa

d o

f 4

Sam

ple

Tra

nsf

orm

ers.

So

urce

: H

EC

O.

So

urce

: H

EC

O.

So

urce

: H

EC

O.

So

urce

: H

EC

O.

(c)

Ind

ust

rial

(a)

Res

iden

tial

(d)

Mix

(b)

Com

mer

cia

l

20

11

20

11

2012

2012

2013

2013

2014

2014

2011

2011

201

2

201

2

20

13

20

13

2

014

20

14

69

Appendix C


Table C.1: Summary Statistics & Difference in Means.

Difference

Variables Mean SD Mean SD in Means p-value

Baseline Consumption (kWh)a 971.37 699.97 1,044.16 616.82 -72.79 0.0005

Maximum Solar Irradiance (W/m2)b 205.32 11.94 205.83 11.78 -0.51 0.1836


Home Value ($/square foot)c 504.45 196.03 448.90 167.82 55.55 0.0000

Age of Homes (years)d 45.21 15.88 42.28 16.23 2.93 0.0000

Home Size (sqft) 1,913.19 923.28 2,225.20 985.54 -312.01 0.0000

Home Energy Intensity (kWh/Sqft)e 0.55 0.33 0.50 0.26 0.04 0.0001

Demographics

Education (% College Degree or Higher) 38.52 17.46 39.29 17.05 -77% 0.1654

Family Size 3.27 0.75 3.25 0.74 0.02 0.3900

% Owner-Occupied Housing Units 73.65 17.50 73.83 16.88 -18% 0.7449

Median Household Income ($) 93,112.52 27,213.31 94,871.39 26,782.92 -1,758.87 0.0434

Median Age 43.43 7.48 43.05 7.51 0.37 0.1219

a We use monthly usage from 2000 to 2005 (excluding post-solar observations) to calculate baseline consumption.

b Maximum solar irradiance is the maximum value of monthly solar irradiance available at a household's premise, including the period spanning

from 2003 to 2015.c

Property value per square foot is calculated by dividing a household's property value by home size.d

Age of home is calculated by subtracting 2016 by a home's year built.e

Monthly usage per sqft is calculated by dividing a household's "baseline" consumption by a home size

No PV PV

70

Table C.2: Marginal Effects for the Logit Model.

(1) (2) (3) (4)

Baseline Consumption (kWh) -1.02E-05 -9.56E-06 2.61E-05** 2.25E-05*

(1.29E-05) (1.29E-05) (1.11E-05) (1.28E-05)

Maximum Solar Irradiance (W/m2) 7.22E-04 7.10E-04 7.72E-04 7.53E-04

(6.01E-04) (6.02E-04) (6.04E-04) (6.02E-04)

Home Value ($/square foot) -2.51E-04*** -2.61E-04*** -3.74E-04***

(5.02E-05) (5.00E-05) (4.55E-05)

Age of Home -1.08E-03** -1.47E-03*** -1.28E-03***

(4.68E-04) (4.62E-04) (4.68E-04)

Home Size (sqft) 5.74E-05*** 6.04E-05*** 8.29E-05***

(1.08E-05) (1.07E-05) (9.72E-06)

Education (% College Degree or Higher) 0.011 -0.019 0.225*** -0.107

(0.081) (0.080) (0.059) (0.078)

Family Size -0.030** -0.037** -0.012 -0.030**

(0.015) (0.015) (0.013) (0.015)

Homeownership (% Owner-Occupied Housing Units) -0.049 -0.024 -0.055 -0.010

(0.059) (0.059) (0.054) (0.059)

Median Household Income ($) 6.89E-07 8.00E-07* 5.85E-07

(4.44E-07) (4.42E-07) (4.46E-07)

Median Age -0.003** -0.004*** -0.002 -0.004***

(1.35E-03) (1.33E-03) (1.33E-03) (1.33E-03)

Having Solar Water Heater = 1 0.361*** 0.362*** 0.363*** 0.366***

(0.014) (0.014) (1.36E-02) (1.34E-02)

Notes: This table shows the marginal effects of the logistic regression The dependent variable is a binary variable equals 1 if a

household installed solar PV and 0 otherwise. The total number of households is 4,047, where 1,557 are non-PV and 2,490

are PV households. Standard errors are shown in parentheses. *,**, and *** indicates significance at the 90%, 95%, and

99% level, respectively.

Dependent Variable: Adopt Solar = 1 and 0 Otherwise

71

Appendix D


Figure D.1: HECO/AWS Virtual Gridded Data Map – Oahu.

Figure D.2: SolarAnywhere Data Map – Oahu.

72

Figure D.3: Estimated Monthly Solar Irradiance – A Sample Grid-Tile Data Point.

Glo

bal

Hori

zon

tal

Irra

dia

nce

(W

/m2)

73

Figure D.4: Annual & Cumulative PV Installations (Samples).

74

Figure D.5: Average PV Module Price & Total PV Installation Cost.

75

Figure D.6: PV System Size Distribution.35

35 Figure D.6 additionally shows how population average of PV system size (average system size of all

residential NEM customers in Hawaii) on each year mostly lies within 50% of the sample’s PV system

size distribution.

76

Figure D.7: Percent Energy Offset from PV.

77

Figure D.8: Housing Characteristics.

(a) Age of Home.

(b) Home Value. (c) Home Size.

(d) Baseline Consumption. (e) Energy Intensity.

78

Figure D.9: Households’ Demographics.

(a) Median Age.

(b) Median Income. (c) Homeownership.

(d) Education. (e) Family Size.

79

Appendix E

Random Sampling Methodology

The following section summarizes the random sampling procedures used in this dissertation. The

purpose of this was to develop characteristics and estimates of electricity consumption of

residential customers, both with and without rooftop PV, using samples randomly selected within

each category. Let Custo be the total number of residential customers on Oahu and

Custo = PVo + NoPVo

where PVo and NoPVo are the number of residential customers on Oahu with and without solar

PV installation, respectively. Let the index c represent circuit (strata) c on the Oahu electrical

grid, where c = 1, 2, 3, …, b and b is the total number of circuits consisting of at least one

residential customer (for Oahu b = 323). Let Custc be the number of residential customers on

circuit c and

Custc = PVc + NoPVc

PVo = ∑ PVcbc=1 and NoPVo = ∑ NoPVcb

c=1

where PVC and NoPVc are the number of residential customers on circuit c with and without

solar PV installation, respectively.

For the purposes of this dissertation, assume the initial sample consisted of 2,500 non-PV

residential customers and 3,000 PV residential customers. In order to ensure that a representative

number of customers was selected from each circuit, the number to select from each was

calculated as follows:

𝑁𝑐𝑃𝑉 =

𝑃𝑉𝑐

𝑃𝑉𝑜 *3,000 and 𝑁𝑐

𝑁𝑜𝑃𝑉 = 𝑁𝑜𝑃𝑉𝑐

𝑁𝑜𝑃𝑉𝑜 *2,500

where 𝑁𝑐𝑃𝑉 and 𝑁𝑐

𝑁𝑜𝑃𝑉 are the number of residential samples with and without solar PV

installation on circuit c, respectively.

80

Appendix F


Table F.1: Summary of Electricity Demand Studies.

Author(s) Country Study Period Data Methodologya

Price Elasticityb

Halvorsen (1975) USA 1961-1969 Annual Static,Dynamic Models -1.52

Filippini (1999) Switzerland 1987-1990 Annual OLS,LSDV,ECM -0.30

Bose and Shukla (1999) India 1985-1993 Annual Static,Dynamic Models -0.65

Bjørner et al. (2001) Denmark 1983-1996 Annual FE -0.40

Al-Faris (2002) GCCc

1970-1997 Annual Cointegration,ECM -0.18 to -0.04

Filippini and Pachauri (2004) India 1993-1994 Monthly OLS -0.51 to -0.29

Kamerschen and Porter (2004) USA 1973-1998 Annual PAM,SE -0.94 to -0.85

Holtedahl and Joutz (2004) Taiwan 1955-1995 Annual Cointegration,ECM -0.16

Narayan and Smyth (2005) Australia 1969-2000 Annual ARDL -0.26

Reiss and White (2005) California 1993-1997 Annual GMM,OLS -0.39 to -0.28

Bernstein et al. (2006) USA 1977-2004 Annual PAM -0.31 to -0.04

Halicioglu (2007) Turkey 1968-2005 Annual Cointegration,ARDL -0.46 to -0.33

Atakhanova and Howie (2007) Kazakhstan 1994-2003 Annual Panel GMM -0.22 to -1.10

Erdogdu (2007) Turkey 1984-2004 Quarterly PAM,Cointegration -0.04 to -0.01

Dergiades and Tsoulfidis (2008) USA 1965-2006 Annual ARDL -0.39

Ziramba (2008) South Africa 1978-2005 Annual Cointegration,ARDL -0.02

Paul et al. (2009) USA 1990-2006 Monthly PAM -0.21 to -0.05

Sa'ad (2009) South Korea 1973-2007 Annual STSM,Kalman Filter -0.14

Amusa et al. (2009) South Africa 1960-2007 Annual Cointegration,ARDL -0.04

Athukorala and Wilson (2010) Sri Lanka 1960-2007 Annual Cointegration,ECM -0.16

Alberini et al. (2011) USA 1997-2007 Annual PAM -0.89 to -0.74

Fan and Hyndman (2011) Australia 1997-2008 Half-Hourly Semi-PAA -0.43 to -0.36

Alberini and Filippini (2011) USA 1995-2007 Annual PAM -0.15 to -0.08

Lee and Chiu (2011) OECDd

1978-2004 Annual PSTR -0.23

Dilaver and Hunt (2011) Turkey 1960-2008 Annual STSM -0.38

Labandeira et al. (2012) Spain 2005-2007 Monthly GLS -0.25 to -0.03

Zhou and Teng (2013) China 2007-2009 Annual OLS -0.50 to -0.35

Blázquez et al. (2013) Spain 2000-2008 Annual PAM -0.11

Okajima and Okajima (2013) Japan 1990-2007 Annual PAM -0.39

Lim et al. (2014) South Korea 1970-2011 Annual Cointegration,ECM -0.42

Arisoy and Ozturk (2014) Turkey 1960-2008 Annual TVP,Kalman Filter -0.02

a ARDL = Autoregressive distributive lag, ECM = Error correction model, FE = Fixed-effects estimator, GLS = Generalized least squares,

GMM = Generalized method of moments, LSDV = Least square dummy variable, OLS = Ordinary least squares, PAM = Partial adjustment

model, PSTR = Panel smooth transition regression, SE = Simultaneous equation, Semi-PAA = Semi-parametric additive model, STSM =

Structural time series model, and TVP= Time varying parameter approach b This table reports short-run residential price elasticities of electricity demand only.

c GCC stands for Gulf Cooperation Council which includes Saudi Arabia, United Arab Emirates, Kuwait, Oman, Bahrain, and Qatar.

d 24 OECD countries include Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy,

Japan, South Korea, Luxembourg, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, and USA.

81

Table F.2: Summary Statistics of Monthly Electricity Usage – PV & No PV

Table F.3: Summary Statistics of Other Variables.

Mean SD Min Median Max

Baseline Period: Jan 2000 to Dec 2009

No PV 957.02 726.20 96 783 12,640

Pre-Solar PV 1,041.91 653.87 72 884 9,920

Overall Period - Jan 2000 to May 2016

No PV 907.13 697.23 93 736 12,640

Pre-Solar PV 1,034.69 650.79 72 878 9,920

Post-Solar (Gross) PV 906.33 598.95 80 755 8,689

Post-Solar (Net) PV 192.41 402.17 -2,240 107 6,320

Notes: Net monthly usage is the difference between the amount of energy delivered from the grid to customers'

homes and the excess energy generated from PV systems being sent back to the grid. Gross monthly usage is the sum

of net monthly usage and the estimated PV energy output.

Monthly Usage (kWh)

Mean SD Min Max

Real Electricity Price (cents/kWh) 25.44 6.26 16.28 37.58

Maximum Temperature (F) 87.26 2.83 82 93

Total Precipitation (inches) 1.36 2.13 0.01 16.92

Average Wind Speed (mph) 9.8 1.88 5 13

PV System Size (kW)a 5.05 3.33 0.28 35.90

a Initial PV sytem size (kW) - nameplate capacity

Prices, Weather & PV

82

Table F.4: Summary Statistics of Monthly Electricity Usage – By PV Sizing Group.

Mean SD Min Median Max

No PV 957.02 726.20 96 783 12,640

Pre-Solar PV - Net Import 1,166.04 756.75 103 974 9,920

PV - Net Zero 979.73 599.20 72 834 8,640

PV - Net Export 661.81 489.48 111 527 4,913

No PV 907.13 697.23 93 736 12,640

PV - Net Import Pre-Solar 1,174.19 757.41 103 983 9,920

Post-Solar (Gross) 937.70 650.71 80 766 8,038

Post-Solar (Net) 324.68 446.53 -1,911 216 6,320

PV - Net Zero Pre-Solar 966.46 589.84 72 823 8,640

Post-Solar (Gross) 900.93 606.59 93 741 8,689

Post-Solar (Net) 46.75 295.51 -2,240 3 4,080

PV - Net Export Pre-Solar 633.38 462.93 102 506 4,913

Post-Solar (Gross) 704.53 478.69 101 573 3,016

Post-Solar (Net) -98.63 278.38 -1,684 -74 1,073

Notes: Net monthly usage is the difference between the amount of energy delivered from the grid to customers' homes and

the excess energy generated from PV systems being sent back to the grid. Gross monthly usage is the sum of net monthly

consumption and the estimated PV energy output.

Monthly Usage (kWh)

Baseline Period: Jan 2000 to Dec 2009

Overall Period - Jan 2000 to May 2016

83

Table F.5: Empirical Results for Electricity Demand Model (3.8) and (3.9).

(1) (2) (3)

Baseline Overall Overall

2000-2009 2000-2016 2000-2016

ln(Pricet-1) -0.117*** -0.099*** -0.099***

(0.008) (0.007) (0.007)

ln(Pricet-1)*PV 0.006 -0.043*** -0.004

(0.011) (0.013) (0.013)

ln(Pricet-1)*PV*PostPV -0.111*** -0.067***

(0.032) (0.032)

ln(Temperature) 0.221*** 0.244*** 0.244***

(0.027) (0.023) (0.023)

ln(Wind) -0.020*** -0.028*** -0.028***

(0.002) (0.002) (0.002)

ln(Precipitation) -8.14E-04*** 0.003*** 0.003***

(3.10E-04) (2.46E-04) (2.46E-04)

ln(Temperature)*PV 0.106*** 0.126*** -0.186***

(0.036) (0.033) (0.034)

ln(Wind)*PV -0.003 -0.024*** 0.014***

(0.003) (0.002) (0.003)

ln(Precipitation)*PV 2.85E-04 0.005*** 0.001

(4.16E-04) (3.59E-04) (3.62E-04)

ln(Temperature)*PV*PostPV 1.325***

(0.044)

ln(Wind)*PV*PostPV 0.015***

(0.005)

ln(Precipitation)*PV*PostPV 0.008***

(6.83E-04)

Notes: This table shows the results of the demand regression in equation (9) and (10), with

fixed effect and control variables specified in the equation. The dependent variable is the log of

gross electricity consumption. The sample period is from January 2000 to May 2016. The total

number of households is 3,650, where 1,557 are non-PV and 2,093 are PV households. PV is a

dummy variable equals 1 if a household had installed PV at some point in the study period.

PostPV is an indicator equals 1 for the period after a household had installed solar PV. Standard

errors in parentheses are clusteres at the household level to adjust for serial correlation. *,**,

*** indicates significance at the 90%, 95%, and 99% level, respectively.

Period Considered

Dependent Variable: Log of Gross Electricity Consumption

84

(4)

(5)

(6)

(4)

(5)

(6)

(4)

(5)

(6)

Base

line

Overa

llO

vera

llB

ase

line

Overa

llO

vera

llB

ase

line

Overa

llO

vera

ll

20

00

-20

09

20

00

-20

16

20

00

-20

16

20

00

-20

09

20

00

-20

16

20

00

-20

16

20

00

-20

09

20

00

-20

16

20

00

-20

16

ln(P

rice

t-1)

-0.1

41***

-0.1

22***

-0.1

19***

ln(T

em

pera

ture

)0.1

83***

0.1

61***

0.1

77***

(0.0

09)

(0.0

07)

(0.0

07)

(0.0

29)

(0.0

26)

(0.0

26)

ln(P

rice

t-1)*

NI

0.1

11***

0.1

06***

0.1

24***

ln(T

em

pera

ture

)*N

I0.3

56***

0.5

54***

0.2

16***

ln(T

em

pera

ture

)*N

I*P

ost

PV

-0.4

66

(0.0

20)

(0.0

19)

(0.0

19)

(0.0

66)

(0.0

65)

(0.0

65)

(0.4

20)

ln(P

rice

t-1)*

NZ

0.0

13

-0.0

14

0.0

25*

ln(T

em

pera

ture

)*N

Z0.0

60

0.1

12***

-0.2

27***

ln(T

em

pera

ture

)*N

Z*P

ost

PV

-0.2

25

(0.0

13)

(0.0

15)

(0.0

15)

(0.0

44)

(0.0

41)

(0.0

42)

(0.4

20)

ln(P

rice

t-1)*

NE

-0.2

20***

-0.2

56***

-0.2

03***

ln(T

em

pera

ture

)*N

E-0

.257

-0.2

56

-0.6

63***

ln(T

em

pera

ture

)*N

E*P

ost

PV

1.6

43***

(0.0

85)

(0.0

69)

(0.0

73)

(0.2

25)

(0.2

29)

(0.2

21)

(0.4

14)

ln(W

ind)

-0.0

23***

-0.0

32***

-0.0

31***

(0.0

02)

(0.0

02)

(0.0

02)

ln(P

rice

t-1)*

NI*

Post

PV

-0.2

25***

-0.1

86***

ln(W

ind)*

NI

0.0

09**

-0.0

10**

-0.0

05

ln(W

ind)*

NI*

Post

PV

0.0

46

(0.0

30)

(0.0

30)

(0.0

04)

(0.0

04)

(0.0

04)

(0.0

41)

ln(P

rice

t-1)*

NZ

*P

ost

PV

-0.1

84***

-0.1

22***

ln(W

ind)*

NZ

0.0

01

-0.0

20***

-0.0

09***

ln(W

ind)*

NZ

*P

ost

PV

0.0

44

(0.0

35)

(0.0

36)

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

41)

ln(P

rice

t-1)*

NE

*P

ost

PV

-0.1

22*

0.0

19

ln(W

ind)*

NE

-0.0

18

-0.0

52***

-0.0

24

ln(W

ind)*

NE

*P

ost

PV

-0.0

27

(0.0

64)

(0.1

24)

(0.0

17)

(0.0

16)

(0.0

16)

(0.0

41)

ln(P

reci

pit

ati

on)

-0.0

01***

0.0

03***

0.0

03***

(3.3

8E

-04)

(2.6

6E

-04)

(2.6

6E

-04)

ln(P

reci

pit

ati

on)*

NI

0.0

01

0.0

04***

2.8

2E

-04

ln(P

reci

pit

ati

on)*

NI*

Post

PV

-0.0

13**

(0.0

01)

(0.0

01)

(0.0

01)

(0.0

06)

ln(P

reci

pit

ati

on)*

NZ

0.0

01*

0.0

06***

0.0

01*

ln(P

reci

pit

ati

on)*

NZ

*P

ost

PV

-0.0

11*

(0.0

01)

(4.3

9E

-04)

(4.5

4E

-04)

(0.0

06)

ln(P

reci

pit

ati

on)*

NE

-0.0

01

0.0

07**

-3.6

2E

-04

ln(P

reci

pit

ati

on)*

NE

*P

Post

PV

0.0

20***

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

05)

Note

s: T

his

table

sho

ws

the

resu

lts o

f th

e dem

and r

egre

ssio

n in

equa

tion

(11)

and (

12),

with

fix

ed e

ffec

t an

d c

ont

rol v

aria

ble

s sp

ecifi

ed in

the

equa

tion.

The

dep

enden

t va

riab

le is

the

log

of gr

oss

ele

ctrici

ty

cons

umptio

n. T

he s

ample

per

iod is

fro

m J

anua

ry 2

000 to M

ay 2

016. T

he tota

l num

ber

of ho

useh

old

s is

3,6

50, w

here

1,5

57 a

re n

on-

PV

and

2,0

93 a

re P

V h

ous

ehold

s. O

f th

ese

PV

hous

ehold

s, 8

61 a

re N

et

Import

, 1,1

88 a

re N

et Z

ero, an

d 4

4 a

re N

et E

xport

hous

ehold

s. P

V is

a d

umm

y va

riab

le e

qua

ls 1

if a

hous

ehole

had

inst

alle

d P

V a

t so

me

poin

t in

the

stu

dy

per

iod.

Post

PV

is a

n in

dic

ator

equa

ls 1

for

the

per

iod

afte

r a

hous

ehold

had

inst

alle

d s

ola

r P

V. S

tand

ard e

rrors

in p

aren

thes

es a

re c

lust

eres

at th

e ho

useh

old

leve

l to a

dju

st for

serial

corr

elat

ion.

*,*

*, an

d *

** in

dic

ates

sig

nific

ance

at th

e 90%

, 95%

, an

d 9

9%

leve

l,

resp

ectiv

ely.

Pe

rio

d C

on

sid

ere

d

Dep

en

den

t V

ari

ab

le:

Lo

g o

f G

ross

Ele

ctr

icit

y C

on

sum

pti

on

Tab

le F

.6:

Em

pir

ical

Res

ult

s fo

r E

lect

rici

ty D

em

an

d M

od

el (

3.1

0)

an

d (

3.1

1).

85

Appendix G


Figure G.1: Electricity Prices & Brent Crude Oil Price.

86

Fig

ure

G.2

: A

ver

ag

e M

on

thly

Ele

ctri

city

Usa

ge.

87

Figure G.3: Percent Energy Offset by PV – By PV Sizing Group.

Figure G.4: PV Installation Trend – By PV Sizing Group.

88

Figure G.5: 12-Month Pre-Solar Monthly Usage.

Figure G.6: PV System Size Distribution.

89

Fig

ure

G.7

: A

nn

ual

Aver

age

Usa

ge

& P

ercen

t Y

ear-

ov

er-Y

ear

Ch

an

ge.

90

Figure G.8: Consumption Trend – 2 Years Before & 4 Years after Installation.

Figure G.9: The Rate of Change in Electricity Consumption after PV Installation.

91

Figure G.10: Percent Exported Energy Relative to PV Energy Production

(Kernel Density Distribution).

Figure G.11: Net Monthly Electricity Consumption.

Den

sity

Den

sity

92

Appendix H

Additional Information

Figure H.1: PV System Size Distribution – Sample VS Population (Oahu).

93

Fig

ure

H.2

: G

ross

Ele

ctri

city

Con

sum

pti

on

Calc

ula

tion

.

94

Fig

ure

H.3

: A

ver

ag

e M

on

thly

Ele

ctri

city

Con

sum

pti

on

– N

o-P

V &

PV

.

95

Fig

ure

H.4

: A

ver

ag

e M

on

thly

Ele

ctri

city

Con

sum

pti

on

– N

o-P

V &

PV

Siz

ing G

rou

p.

96

Figure H.5: Percentage Change from Pre-Solar Usage – Net Import.

97

Figure H.6: Percentage Change from Pre-Solar Usage – Net Zero.

98

Figure H.7: Percentage Change from Pre-Solar Usage – Net Export.

99

Fig

ure

H.8

: P

erce

nta

ge

Ch

an

ge

from

Pre-S

ola

r U

sage

– S

epara

ted b

y P

erce

nt

En

ergy

Off

set

100

Table H.9: PV Sizing Categories – Sensitivity Analysis.

Count % Count %

Net Import 859 41.0% Net Import 920 44.0%

Net Zero 1,190 56.9% Net Zero 1,130 54.0%

Net Export 44 2.1% Net Export 43 2.1%

Count % Count %

Net Import 1,570 75.0% Net Import 1,761 84.1%

Net Zero 509 24.3% Net Zero 325 15.5%


Count % Count %

Net Import 423 20.2% Net Import 374 17.9%

Net Zero 1,319 63.0% Net Zero 1,240 59.2%


Note: The tables above show how the number of customers in each PV sizing group

changes with different indices and different pre-solar period. On the left hand side, the

tables show the number of PV customers under each sizing category based on 1-year

pre-solar monthly consumption. Taking into account any unobserved variations in

energy consumption, the right-hand-side tables show slightly different results when

2-year pre-solar usage is used.

Average (1 year Pre-Solar) Average (2 year Pre-Solar)

Maximum (1 year Pre-Solar) Maximum (2 year Pre-Solar)

Minimum (1 year Pre-Solar) Minimum (2 year Pre-Solar)

101

Table H.10: Number of Households with Additional Solar PV Installations.

Table H.11: Transitions across Sizing Groups – PV Households with Additional Systems.

Table H.12: Number of Households with & without Solar Hot Water Heater (SWH)

1 2 3 4 5

Net Import 863 281 62 9 1

Net Zero 1,187 44 0 0 0

Net Export 44 0 0 0 0

Total 2,094 325 62 9 1

Number of Additional PV Systems

Sizing Group Count %

Under-Under 95 3.81%

Under-Right 177 7.11%

Under-Over 9 0.36%

Right-Under 1 0.04%

Right-Right 31 1.24%

Right-Over 12 0.48%

Under-Under-Under 9 0.36%

Under-Under-Right 41 1.65%

Under-Under-Over 2 0.08%

Under-Right-Right 8 0.32%

Under-Right-Over 2 0.08%

Under-Under-Under-Under 1 0.04%

Under-Under-Under-Right 3 0.12%

Under-Under-Right-Right 3 0.12%

Under-Right-Right-Right 1 0.04%

Under-Right-Right-Over 1 0.04%

Under-Under-Under-Right-Over 1 0.04%

No Add-Ons 2093 84.06%

Note: Under = Net Import, Right = Net Zero, and Over = Net Export

Sizing groups calculation is based on pre-installation consumption.

No PV Net Import Net Zero Net Export

With SWH 104 499 376 35

No SWH 1,453 716 855 9

Number of Samples

102

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